एस्लाम टेल्याONArikum students the things which we had done in the last lecture. In fact, take many table the Khanatha, just may we compare different CMOS and TTL gates and we look at the actual values. So let us start our discussion by revising the contents which we had studied in the last lecture. The operational characteristics were four or five important parameters. The first parameter was DC supply voltage. So every circuit needs a DC supply voltage so that it works. So we usually use 5 volts for TTL for 5 volts supply voltage. Similarly, we need 5 volts for CMOS. There is another series of CMOS in which we need 3.3 volts supply voltage. Then we talked about the noise margin. Noise margin was that every logic level, high or low, it is represented by certain voltage levels. So if that signal is within those voltage levels, then the whole circuit will work well. But due to some external noise, some other factors, the logic 1 or logic 0 representation comes out of that voltage range. Due to that, the circuit might not work. So we had calculated the noise margins. We saw that the 5 volt version of CMOS has more noise margins. That means it can work very well in a noisy environment. The third parameter which we looked at was the power dissipation. Every circuit uses power. Of course, current flows in it. It needs energy. How many watts are consumed in it. So we looked for TTL and CMOS. The power requirement for TTL is more or less fixed. Power requirement for CMOS varies with respect to frequency. Because there is a capacitive load in CMOS circuits. When there is a capacitor, there will be a charge and a discharge. The discharge depends on the frequency it operates. When the frequency of a CMOS circuit increases, the power dissipation also increases. So the variable power dissipation of CMOS circuits will be there. When we measure it, there will be a static power dissipation and a dynamic power dissipation. We will see that in the table. We saw another parameter, the propagation delay. We said that if there is a variable on the input, then after a special delay, you will get a value on the output. So the delay would determine how fast a signal can change at the input of any gate. If the delay factor is changing at a high frequency, then it will not work. We talked about a product of the speed and dissipation. In both the products, there will be a number. You can compare it with different gates. Finally, we saw the fan out. Fan out is how many gates can we connect to the output of another gate. We said it depends on the current which the gate can supply to the inputs of different gates. Again, there is a restriction. There are fixed number of fan outs in TTL. CMOS depends on the frequency. If you want to operate the circuit at a high frequency, then your fan out will be less. That means you will have to connect less number of gates. If you want to operate at a low frequency, then you can connect more number of gates to the output of a gate. These were the five important parameters. Let us have a look at the table where we compare different gates and see the actual numbers. After that, we will start the Boolean algebra. Let us first consider the TTL series of gates. We have the 7-4 standard gate, the 7-4S short key gate, the 7-4LS the low power short key, 7-4AS the advanced short key, and the 7-4ALS the advanced low power short key, and the 7-4F the fast version of TTL. If we look at the propagation delays, the standard version has a propagation delay of 9 nanoseconds, which is almost the highest propagation delay. 7-4LS propagation delay is 9.5 nanoseconds. Fast and ALS are very low. AS is also very low, it is 1.7. If we look at the power dissipation, let us measure in milliwatts, the 7-4S short key power dissipation is more than 20. Low power short key power dissipation is 2, the advanced low power short key power dissipation is 1.2. An important parameter is the speed power product. Let us measure in pico joules. Let us look at these. 4.8 is the lowest of ALS. So, this gate is better than all, in terms of power dissipation and propagation delay. The standard version is the highest, it is 90. Maximum clock rate on which you can operate is also given. Standard TTL gate operates at 35 MHz. The advanced short key operates up to 200 MHz. The advanced low power short key operates up to 70 MHz. Fan out, again 7-4 standard 10 gates can be connected. The short key 20 gates can be connected. The advanced short key 40 gates can be connected. Let us now look at the CMOS series. First, let us look at the 5V series, and then look at the 3.3V series. In the 5V series, you have the 7-4AC and the 7-4AHC. Propagation delay is less compared to TTL logic. Power dissipation is very less. 0.00275 is for 7-4HC. Similarly, 0.0055 is for 7-4AC. CMOS series tells us that power dissipation varies on low frequency and high frequency. Power dissipation static that means no operations or low frequencies. Power dissipation as I have said before is 0.00275. Same gate, if it operates at 100 kHz, its power dissipation increases to 0.0625. Similarly, for 7-4AC, the power dissipation increases to 0.08 at 100 kHz. Speed power product is at 100 kHz. 1.125 is for 7-4AC. 0.4 is for 7-4AC. 0.23 is for 7-4AHC. If we compare the speed power product with TTL, it is very less. Maximum clock rate is 50 for AC. For AC, it is 160 MHz. And for AHC, it is 170 MHz. Now, let us have a look at the 3.3V CMOS series, the 7-4LV, the 7-4LVC and the 7-4ALVC. Propagation delay again are very low, 9, 4.3 and 3 respectively. Power dissipation, the static power dissipation is again very low, 0.0016, 0.0008 and 0.0008 for the 3 gates respectively. Operational clock rate, maximum clock rate is 90, 100 and 150 respectively. We have just looked at some parameters of TTL and CMOS gates. So, by comparing those numbers, you can just see which gate is better and which particular gate is required for your particular implementation. Now, let us start with today's topic, Boolean algebra. Boolean algebra, how is it different from the conventional algebra? Well, Boolean algebra has two values. In conventional algebra, there are many values. Boolean algebra, since it is dealing with binary values, so its value will be 0, and its value will be 1. So, let us start by looking at some definitions of Boolean algebra. In Boolean algebra, we use literal, we talk about complement and we talk about variables. What is a variable? You may use variable programming. It is a symbol which represents a value. So, in Boolean algebra, a variable is usually a capital letter, alphabet letter A, B, C, Z, N. So, it represents a value. What is the value? Either it is going to be a 0 or a 1 because it is, of course, representing a Boolean value or a binary value. What is complement? The inverse of a variable. So, if variable A has the value 0, A bar would have the value 1. So, the bar represents the inverse of the complement. What is literal? Literal could be the variable or its complement. So, let us say B bar is a literal. B is its complement. Again, it is considered to be a literal. So, these are the three definitions which we have to use again and again. Boolean algebra, why are we using it? Basically, why do we use mathematics? One benefit of mathematics is that all real world problems can be represented in the form of equations. What is the benefit? We can check or implement in the form of mathematical equations. Let me give you an example. You take an iron rod let us say 1 inch diameter. You start heating it on one end. And you need to determine that on the other end, let us say 1 foot long rod is there. On the other end, at what time it will be 50 degrees temperature. Now, this entire heating of an iron rod can be modeled using a mathematical equation. Now, if you have an equation then you can perform you do not need to perform an experiment. You do not need to get an actual rod and heat that. Equations say you have different values done or you can calculate a answer. In fact, if you have an equation then you can use different rods different metal rods and different diameter rods. So, mathematics solves the problem. You do not have to use practically anything. Similarly, Boolean algebra allows you to represent digital circuits in terms of expressions. What will be the benefit? One benefit is that let us suppose you have a very complex, complicated circuit having different gates. How will that circuit perform? What output will come? Well, one way is to practically implement that circuit. You will need more time to spend your money on it. So, the easiest way would be to represent that circuit through a Boolean expression a mathematical expression of different input combinations you get the answer. So, you can easily check if that particular circuit is going to work correctly or otherwise. You can use a Boolean expression to simplify circuits. Let us suppose you have a circuit composed of 20 gates it performs a certain function. Now, you could implement the same function using 5 gates. Now, if you implement a circuit having 5 gates that means the circuit is going to be faster less propagation delay the power requirement would be reduced so it would be better than the previous circuit which uses more gates. Now, how would you simplify a circuit? By looking at the circuits it is very difficult to find out the simplified version of that circuit. A better way would be to write an expression of that original circuit and then using the rules and laws of Boolean algebra simplify the expression. You would get a simplified version of the expression and if you directly implement the circuit using that expression you would have a simple circuit. So, let us look at Boolean operations. In the beginning we talked about two Boolean operations which are important and are used throughout Boolean logic. Boolean addition and Boolean multiplication. Boolean addition is performed by an OR gate. So, two input's OR gate is A plus B. A plus B is known as a sum term because we are adding some term. The multiplication is performed by an AND gate. So, if you have a two input AND gate you have a product term A dot B. A dot B is known as the product term because it is a multiplication result. Let us look at some other sum terms and product terms and let us look at what would be the output of this sum term if one of the variables let us first look at Boolean addition. Boolean addition gives us a sum term. A sum term is described as sum of literals. So, as you can see A plus B is a sum term which is in fact a sum of literals.  The third expression A bar plus B bar plus C is again a sum term composed of three literals. Now, a sum term is equal to one if any literal is equal to one considering A plus B A one ho jai here B one ho jai the output is going to be a one. Similarly, A plus B bar ko agar dekh ha jai in me say koi bhi literal agar one ho jai output one ho jai. A sum term is equal to zero if all are equal to zero. So, considering A bar plus B bar plus C the output or the sum term is zero if A bar is zero B bar is zero and C is zero. Similarly, considering the term A plus B bar the output is zero or the sum term is zero if A is zero and B bar is zero. Let us now look at Boolean multiplication. Boolean multiplication results in a product term product term is described as a product of literals. So, you have three product terms as can be seen AB, AB bar and A bar B bar C. Now, a product term is equal to one if all literals are equal to one. So, AB would give you a one result if A is one and B is one. Similarly, AB bar would give you a one result if A is one and B bar is one. A product term is equal to zero if any one literal is equal to zero. So, considering the term the product term A bar B bar C if any one literal is zero the entire term would be zero. So, if A bar is zero or B bar is zero or C is zero or all three terms literals are zeros the product would be zero. We have just looked at Boolean addition and Boolean multiplication we have looked at the sum term and the product term. Now, when you write Boolean expressions and solve Boolean expressions they are solved on the basis of certain rules, laws and theorems. Normal algebra may be it is done according to certain rules and theorems. So, now let us look at some rules and theorems being applied in Boolean algebra. There are three laws being applied in Boolean algebra the associative law the distributed law and the commutative law. These three laws are used in normal algebra and they are used in the same way. Then there are certain rules I think there are about 12 rules again we are going to be looking at those rules. Then we have two theorems So, again we would be looking at the two theorems. So, now let us have a look at the the three laws the rules and the theorems applied in Boolean algebra. The basic laws of Boolean algebra are the same as ordinary algebra and hold true for any number of variables. So, let us start by looking at the commutative law commutative law for addition states that sum of literal and beliteral that is a or b is equal to b or a if you have three literals a b and c the commutative law states that a or b or c is equal to c or b or a. Implementation wise an or gate is used. So, if you have a two input or gate it does not matter if you connect the literal a to the first input or to the second input in both cases the output would be the same. Let us consider the commutative law for multiplication. The commutative law for multiplication states that product of literal a and b is equal to product of b and a. Again implementation wise an and gate is used because multiplication of course is done using and gates. So, according to the commutative law for multiplication it does not matter if you connect the literal a to the first input or the second input of the and gate. The result would always be the same. Again you could have multiple literals a b c and d. The law holds true for multiple literals. Let us now consider the associative law for addition. The associative law for addition states that sum of b and c literals that is b or c odd with a is the same as a or b odd with c. Implementation wise you require a combination of two or gates. So, the inputs are 3 a b and c. So, any of these 3 inputs can be connected to any of the 3 literals a b or c. The output would be the same. Let us consider the associative law for multiplication. The associative law for multiplication states that the product of b and c b and c ended with literal a is the same as the product of literals a b ended with c. Implementation wise you would use a combination of 2 and gates. So, altogether you would have 3 inputs. Any of the 3 literals a b and c can be connected to any 3 inputs. The output would be the same. You could have 4 literals, 5 literals the associative law for multiplication would hold true. The distributive law states that b or c ended with a is equal to a b odd with a c. The left side of the expression that is b or c ended with a can be implemented by using a combination of AND gate and OR gate. The inputs b and c are odd together. The output of the OR gate is connected to an AND gate and the result is b or c ended with a. The right side of the expression a b the product of a b odd with the product of a and c can be implemented using 3 gates 2 AND gates and an OR gate. So, the first AND gate is connected to inputs a and b the product is a b the second AND gate is connected to inputs a and c the product is a c the outputs of the 2 AND gates are connected to an OR gate the output of the OR gate is product a b odd with product a c let us have a look at 12 rules of Boolean algebra the first rule a or 0 is equal to a this can be proved by assigning values to the variable a if a is 0 what is the result the result is 0 if a is 1 what is the result the result is 1 so the output is the same is equal to a the second rule a OR 1 is equal to 1 now by assigning values to the variable a 0 or 1 the output remains a 1 the third rule a product 0 so as we have discussed before anything multiplied by 0 gives you a 0 so a product 0 is equal to 0 the fourth rule a product 1 is equal to a we have studied this before as well anything multiplied by 1 gives you the same thing rule number 5 a OR a is equal to a again this can be proved by applying assigning values to the variable a so if a is 0 so it is 0 or 0 which is equal to 0 if a is 1 then the rule becomes 1 OR 1 the result is 1 rule number 6 OR a bar is equal to 1 again let us apply the two values to the variable a if a is 0 then the equation becomes 0 OR 1 the result is 1 if a is 1 the equation becomes 1 OR 0 the result is again a 1 rule number 7 a product a is equal to 0 again let us check if a has the value 0 so the equation becomes 0 and 0 the result is 0 if a is equal to 1 it is 1 and 1 the result is 1 rule number 8 a and a bar the result is 0 applying the two values if a is equal to 0 0 and 1 the result is 0 similarly if a is equal to 1 the equation becomes 1 and 0 the result is again a 0 rule number 9 a double bar is equal to a double bar means complemented twice so if you have a single bar that means complemented once if you have a double bar you complement the complement again you have just cancelled out the two complements so if a is equal to 0 the answer would remain a 0 if a is equal to 1 the answer would remain a 1 rule number 10 a odd with the product term ab the result is a we can prove this a is common in both the terms if you take a as a common you are left with 1 or b now 1 or b if you apply a rule 2 is equal to 1 so you are left with a product 1 which is equal to a rule 11 a or a bar b which is equal to a or b this can again be proved a can be multiplied with sum of b plus 1 the result is 1 so you you multiply a with 1 it would remain an a so you multiply a with b or 1 you simplify the equation this gives you ab plus a and the previous term a bar b now re-adjusting the expression you have a plus ab plus ab bar b now considering b which is common in terms ab and ab bar b if you simplify this the equation turns out to be a plus b the last rule rule number 12 a or b ended with a or c the result is a odd with the product term b c this can be proved by rewriting the equation so a multiplied by a gives you a a ended with c gives you a c b ended with a gives you a b b ended with c gives you b c now considering the first 3 terms a a c and a b you have a common a so if you remove the common a the remaining portion is equal to 1 so the equation simplifies to a plus b c now let us consider de Morgan's theorems there are 2 theorems the first theorem states the complement of a product of variables to the sum of the complements of the variables in form of an equation a b whole bar is equal to a bar plus b bar de Morgan's theorem the first theorem holds true for any number of variables implementation wise ab whole bar is implemented using anand gate the right side of the equation a bar plus b bar is implemented again by anand gate but the alternate symbol of the anand gate is used let us consider the second theorem de Morgan's second theorem states that the complement of sum of variables is equal to the product of the complements of the variables writing the expression it is a or b whole bar equals to a bar entered with b bar implementation wise you have a nor gate so a nor b gives you a plus b or a or b complemented the right side of the equation a bar entered with b bar can be implemented using the same nor gate but represented in its alternate symbolic form again the second theorem of de Morgan's holds true for multiple variables de Morgan's theorem can be applied to expressions having any number of variables so let us have a look the first expression x and y and z whole bar is equal to x bar plus y bar plus z bar similarly or y or z whole bar is equal to x bar entered with y bar entered with z bar de Morgan's theorem can be applied to a combination of other variables let's have a look at the expression the expression is a or b c this is considered to be a single term entered with another term which is a c odd with b both these terms are complemented so you have an entire bar over the product of the two terms these two terms according to de Morgan's theorem can be written as a plus b c whole bar plus a c plus b whole bar the plus of course indicates the or operation this equation can be further simplified to a bar b c bar plus a c bar b bar this can further be simplified to a bar entered with b bar plus c bar plus b bar entered with sum of a bar and c bar this expression can be further rewritten as a bar odd with a bar b bar odd with b bar c bar final expression is a bar b bar plus a bar c bar plus b bar c bar we have looked at the laws, rules and theorems used in Boolean algebra you need to practice these laws, rules and theorems you need to know about them because we would be applying these rules and laws throughout this course now look at the application of these Boolean expressions to analyze a circuit let us consider an expression a plus b entered with c now what kind of information does this expression convey well a odd or b means it to input or gate is being used the output of this is connected to an AND gate and the other input of the AND gate is connected to the variable c so basically a or b entered with c gives you three variables so if you write out the function of this or gate and AND gate circuit how many columns are there how many possible input combinations how many possible well since there are three input variables therefore you have eight possible combinations what is the output of this circuit again you can analyze that by applying the appropriate inputs let us say you start with the combination 0 0 and 0 so a or a or b is 0 or 0 which is 0 AND it with c anything AND it with 0 gives you a 0 so the output is going to be 0 instead of you using all the eight terms you can find the output just by looking at the equation c is entered with the or of a and b a or b entered with c now if a or b is a 1 and c is a 1 then you would get a 1 output if either a or b is a 0 or c is a 0 you would get a 0 output right so if we know this then we can easily determine for which particular combination of 0s and 1s you would get a 1 output let us have a look at another circuit and let us analyze that circuit using the boolean expression let us consider the expression a and b or with c bar and the entire term entered with d now what type of or what kind of information does this expression convey basically there are 4 variables so the circuit represented by this expression is going to have 4 inputs and of course a single output now by looking at the expression again the variables a and b are entered together 2 input and gate is required the output of the AND gate is ord with c bar that means a and a not gate is required the input of this not gate is connected to c the output of the not gate is c bar so the output of the not gate and the output of the AND gate are connected to the input of an or gate so it is a 2 input or gate the output of the or gate would of course be a and b ord with c bar we have the 4th variable variable d it is entered with the term a b plus c bar so how do we AND d with the a b plus c bar term an AND gate a 2 input AND gate now for which particular combinations of 1s and 0s for the inputs a b c and d the output is going to be a 1 let us again have a look at the expression the output is going to be 1 if d is 1 and the term a b plus c bar is a 1 now how would the term a b be a 1 if a b is a 1 and the little c bar is a 1 how is the AND term a b going to be 1 if both a and b are 1s the little c bar how is that going to be 1 if c is 0 so when do you obtain a 1 output when a is 1 b is 1 c is 0 and d is 1 so for this particular combination of 1s and 0s you obtain a 1 output now this can be verified by drawing out a function table so what is the size of the function table how many input columns are required basically there are 4 variables a b c and d so there are 4 input columns a b c and d how many input combinations are possible since there are 4 variables so 16 different input combinations are possible the output of course is 1 represented by f now let us write all the outputs for each of these 16 combinations starting with the first combination of 0 0 0 the output is 0 why because d is 0 considering the second input 0 0 0 1 now in this particular case d is 1 and c is 0 so both the conditions are satisfied the answer is or the output is 1 similarly for the input condition 0 1 0 1 again d is 1 and c is 0 the conditions are satisfied the output is again going to be a 1 let us consider the input 1 0 0 1 again d is 1 c is 0 the conditions are satisfied the output is again going to be a 1 let us consider inputs the inputs 1 1 0 1 in this particular case d is 1 c is 0 a and b are both 1s so all 4 conditions are satisfied the output is going to be a 1 the last input combination 1 1 1 1 d is a 1 c is a 1 so this particular condition is not satisfied but a and b both are 1s therefore the output is again going to be a 1 we have looked at 2 examples of analyzing boolean circuits or logic circuits using boolean expressions basically we would be using this method to analyze different circuits throughout the course so it is important that you learn to use these expressions to analyze circuits I would suggest you just write any simple expression of 3 or 4 variables then try to decipher that expression you implement a circuit from that which gates are there then I would suggest that you look at the expression and see which particular combination of inputs you get a 1 output you can verify if you make it a function table so if you have 4 variables in your expression you will get 4 columns 16 combinations all 16 combinations are written you calculate the output using the circuit you verify it by applying those values in the expression so both the things will verify each other so it is important that you practice with the analysis of circuits using these boolean expressions now the other thing which we said we use the expression is to simplify circuits if a circuit is made you will not be able to see it by simplifying it so the best way is to write an expression representing that circuit then apply the rules of boolean algebra laws and theorems which we have discussed that would give you a simpler expression when you have that simple expression then of course you can always implement a circuit using that expression the expression which we are going to use and simplify in the example is a 3 variable expression it represents a large circuit we are going to be simplifying this expression using the rules laws studied so far we would get a simpler expression then we would implement that expression we would obtain a circuit which of course would be very simple as compared to the original circuit the functionality of both the circuits would of course be the same so let us have a look the expression is composed of 3 terms the term b the second term b or c and it with a and the third term b or c and it with b if you simplify this expression consisting of 3 terms you have a b odd with a b odd with a c odd with b b odd with b c now some of these terms simplify is common so you just remove one of the terms b b simplifies to b so you end up with an expression a b odd with a c odd with b odd with b c this expression can be further simplified b and the term b c you have a common b so you end up with b ended with 1 plus c 1 plus c is equal to 1 so you end up with the term b now you have the expression a b odd with a c odd with b now b is the common literal in the terms a b and b so if you simplify these 2 terms you end up with literal b so the expression is b c let us have a look at the circuits represented by the original expression having the 3 terms and the simplified expression having the 2 terms b odd ac the original circuit is made up of 3 AND gates and 2 OR gates the OR gate used at the input has 2 inputs and the OR gate used at the output has 3 inputs altogether you require 5 gates let us now look at the simplified expression and the circuit resulting out of that simplified expression only 2 gates are required an AND gate and an OR gate so you have removed 3 gates the circuit is simpler less power is required and perhaps it is faster than the original circuit we have just looked at an example of simplification of Boolean expressions to implement simpler circuits again this method would be used throughout the course you would be writing expressions you would be simplifying them to simplify and implement simpler circuits so I would advise that you practice you just write some expressions you implement a circuit which represents that expression and then you simplify the expression and then implement the circuit you have to confirm that both the circuits are working how do you do that of course you can do the function through the tables you can check the values in both the expressions now we have been writing expressions different types of expressions there are 2 standard ways of writing expressions one is the sum of products form sum form before we look at the 2 ways of writing these expressions let me describe what is the sum of product form you have already been writing expressions in this form basically you have product terms abc it is a product term de bar it is another product term so abc plus de bar it is sum of product terms you have sum them up this kind of expression basically how you implement basically you would be using a combination of and gates and an or gate product terms by using and gates in all the terms when you add you would use an and gate let us look at the product of some terms product of some terms at the name indicates is some terms which are ended together so let us consider the sum term a plus b it is the sum term because you are implementing an or operation between 2 variables you have another sum term c or d now if you end these 2 terms together that is a or b ended with c plus d you get the sum of rather the product of some terms implement kase keringe you would be using a combination of or gates and and gate you sum terms a implement keringe using or gates in saaron ka joh output hai that would be connected to a single and gate let us have a look at an example which shows the representation of different sum of product terms and product of sum terms but before we do that normally any expression can be easily converted into a sum of product term expression let us look at sum of products form first there are 3 expressions the first expression is a and b odd with a b c so you have 2 product terms and they are odd together the second example is you have 3 product terms product term a b c the second product term c d e and the third product term b bar c d bar now all these 3 product terms are implemented using 3 gates 3 and gates and each of these 3 and gates have 3 inputs sum of products is implemented by using a single or gate having 3 inputs the third example is a bar b the second product term in this example is a bar b c bar and the third term is a c again a combination of and gates and a single or gate is used you would require 2 and gates having 2 inputs and a single and gate having 3 inputs you would of course require a single 3 input or gate now let us look at examples of product of sums form again there are 3 expressions the first expression has 2 sum terms which are multiplied together so the first term is a bar odd with b the second term sum term is a odd with b bar odd with c now both these 2 terms are ended together to give you the second expression has 3 sum terms the first sum term has a bar plus b bar plus c bar the second sum term is c plus d bar plus e and the third sum term is b bar plus c plus d all these sum terms are ended together now how many or gates and and gates are required well there are 3 or terms 3 or gates are required what should be the inputs of these or gates basically in each sum term there are 3 variables so 3 input or gates are required now the final expression is product of these 3 sum terms so you need to have 3 input and gate to and all the 3 sum terms the last expression again has 3 sum terms the first sum term is a plus b the second sum term is a plus b bar plus c and the third sum term is a bar plus c again 3 or gates are required 2 or gates have 2 inputs and a single or gate has 3 inputs the outputs of all these 3 gates are ended together by using a single 3 input and gate the implementation of the first sum of product expression again 2 and gates are used and a single or gate is used the second diagram shows the implementation of the product of sum terms 3 or gates are used and the results or the outputs of these or gates are ended together to gives you the product of sum terms any general expression can be added to the standard sum of product form let us consider the expression a b plus b ended with the sum of c d plus e f so you have a product term c d plus e f this entire term is ended with b and this entire term is added with the product term a b now if you simplify this you end up with a b c d plus b e f the original expression is not in the standard s o p form the simplified version has been converted into the standard sum of product form let us consider the second example you have 2 sum terms ended together so the first sum term is a plus b the second sum term is b plus c plus d now to convert this expression into the standard sum of product form you simplify the expression so you end up with the terms a b odd with a c odd with a d plus b plus b c plus b d if you simplify this expression removing the common terms you end up with a c plus a d plus b which is the standard sum of products form the third expression is a plus b bar odd with c whole bar now this is not a standard sum of products form now this has to be simplified so you end up with a plus p double bar ended with c bar now what did we say when you have double bars over an expression basically both the bars are removed so in this particular case a plus b double bar is simplified to a plus b and c bar remains as it is now if you simplify the expression you end up with a c bar plus b c bar so you have converted the original general expression into sum of products form today we have looked at boolean algebra we have simplified boolean expressions using some tools which we have studied we have also looked at simplifying circuits using boolean expressions we will continue with these boolean expressions in the next lecture hope to see you again for the half is aslam aleykum


Ddweud wrth gwrs. Welcome to the third session of the Culture Tourism Europe and External Relations Committee in session 5. I would like to remind members and the public to turn off mobile phones, and any members using electronic devices to access committee papers during the meeting should ensure that their switch to silent. Today we take evidence in a round table format on the implications of the EU referendum for Scotland. I would like to welcome all our witnesses to pan sefydlu gynnwys yn felly ymddai, ond gweithio'r pwyntiau i alsiwyr. Wrth gwrs, mae'n iawn i'n ei gweld i ddefnyddio, dwi'n ei fod diodell, ddych chi'n credu i Gwyrdd Macallpine MSP gan Ysgol kolonau, a dyna'n gwneud hynny bei'n ffwynd авereu. Fyonor Ross Ysgol kolonau yn ni'n nhw i'n gwneud hynny fe gwyllwch yr ysgol ysgolol ysgolol. Gwymeth hynny yn gwneud hynny i gwyllwch ar y sgolol ysgolol. Mhap, MSP, Fforshout Scotland region. Hydi Vistasen, Ynrys Scotland, executive member. Richard Lochhead, MSP for Murray. Morheena Sinclair-Chin, here at the Law Society of Scotland. Jackson Carlaw, MSP for Eastwood. Elster Sim, director of University Scotland. Gary Clark, head of policy and research at Scottish chambers of commerce. Tary Scott, MSP for Shetland. I'm Helen Martin, I'm an assistant secretary at the STUZ. Ross Greer, MSP for the West of Scotland. I'm Claire Slipper, I'm parliamentary officer at NFU Scotland. Rachel Hamilton, MSP for South of Scotland. Ian Gutt, my day job was the chief executive for the Scottish Pallagic Fisherman's Association. For those who don't know what that is, it's a macro on herring, but I've also got another role as the president of the Scottish Fisherman's Federation. I'm wearing that hat today. I'm Stuart McMillan, MSP for Greenrack Island in Burkland. Thank you all very much. Some of you are familiar to the committee. You've given evidence before or you've submitted written evidence, even for this inquiry. Of course, things have moved on quite a bit. Last week, we had the speech from the Prime Minister, outlining the fact that the UK is no longer going to be a member of the single market. I thought that perhaps you would like to give your thoughts on that and other aspects of the Prime Minister's speech. Who would like to start? Yes, Heidi. Obviously, as NU Scotland, we've previously submitted evidence and notions to Parliament in letters and motions that Lib Dems kindly brought forward for us to Parliament. However, we just want to highlight again that the National Union of Students believes that the single market is vital and that the free movement is vital to the benefits of our students coming to Scotland to study. As a European student, I'm quite familiar with that, and I just want to highlight that today, that it's very important to us and that we will do our best to push that on the Prime Minister and the UK Government to make sure that we will go for a softer Brexit as possible. Perhaps Fiona? On that point, at the Scottish Youth Parliament as well, this is a matter of some concern for us, this idea that leaving the European single market will impact negatively on freedom of movement. It's come out very clearly in the research that we've done, that freedom of movement for young people in Scotland is seen as an opportunity, rather than as a threat and it's something that we want to see protected moving forward. We were very glad to see the strong commitment to workers' rights in the speech, but we also feel that that didn't really set out a comprehensive enough plan for wider social rights. There are concerns that perhaps the economic focus that the speech really took might come at the expense of some of those rights to which we are accustomed. As well as that, I think that the premise of the argument to leave the European single market on immigration arguments just doesn't reflect the concerns and priorities of young people in Scotland. There was a poll even last week showing that young people rate immigration as the second least important issue to go into Brexit negotiations by contrast human rights were the second highest. It just doesn't seem to be in line with the concerns of young people across Scotland. You've raised the issue of workers' rights, so I don't know if the SQC would like to come in. We welcomed the commitment in the Prime Minister's speech to workers' rights, but we were reasonably sceptical that that amounted to a strong enough commitment to us, we and our members. We would be keen to see what she will put into the white paper that goes to Parliament on that issue. It is certainly our number one issue, and we are very concerned about the fact that Brexit will be used as a way to reduce hard-won workers' rights within the economy. We know that the European Union provided a very good structure for defence of those rights, and a lot of the issues were driven by European legislation. We were disappointed that the Prime Minister chose to make a media speech rather than go and speak to Parliament. For us, it was extremely disappointing to see a Supreme Court ruling as the only thing that really brought the Prime Minister to a position where she realised that she couldn't make those sorts of decisions on her own. It is essential that the Westminster Parliament gets the opportunity to scrutinise and debate the negotiating priorities for the UK Government. It is absolutely wrong that the Prime Minister should stand up and say that she has decided that we are leaving the single market. That is something that absolutely needs to be scrutinised and debated on in Parliament. Despite the Supreme Court judgment that there is a moral and democratic duty on the UK Government to consult with the devolved institutions to take views from the devolved institutions and to ensure that priorities from Scotland, Wales and Northern Ireland are reflected in negotiating priorities. We think that that will be a test of our democracy going forward, and so far the Prime Minister is not living up to her requirements. Does anyone else want to come in and clear slipper? Hi, and thank you for having me back today. Obviously, from the outset, and if you, Scotland, said that retaining access to the EU market without barriers and any new tariffs or obstacles to trade would be a major priority for our industry, the freedom to set our own appropriate rules for farming was also an important priority, and remaining within the single market would have been the easiest way to retain that. Obviously, now that we know that we are going to be leaving the single market, the focus becomes upon creating the best and the boldest free trade agreement with the rest of the EU that we can possibly get. We saw new export statistics yesterday that said that food and drink exports out of Scotland were worth £1.8 billion in 2015 to the EU, so clearly that is a major issue for us. I am sure that we will come on to the free trade agreements later on, but it is important for me to say that the key concern here is that not only will that place possible restrictions on access to labour, which is a huge issue for our industry, but there is also a concern that an FTA not done correctly could result in an increase in food imports, which could be hugely damaging for our industry. It is not just the loss of provenance of the Scottish label, but it would also export jobs, incomes, communities, welfare standards, environmental responsibilities out of Scotland potentially, and we hope that that is something that is recognised by the UK and Scottish Governments. I think that just remarking on the Prime Minister's speech, I mean in a sense possibly a bit of a mixed bag for us some useful suggestions of direction, but we would really want to see what is carried through in terms of delivery. I think that universities are absolutely dependent on the free flow of talent across borders, both student talent and staff talent, and we were enormously pleased earlier this week when the First Minister and Ms Somerville came to our event to say that Scotland's universities welcome the world and that we really are committed to being as open as possible to the movement of international talent. I think that the Prime Minister did say something useful on that regard. She did say that we want to continue to attract the brightest and best to work or study in Britain and to openness to international talent. It must remain one of his country's most distinctive assets, but we really want to see delivery on that. I think that it is actually quite difficult dynamic on that when, on the one hand, you got that statement of openness, and on the other hand, following Amber Rudd's speech to the Conservative conference, there is still a dynamic that seems to be hitting in a different direction of having a more restrictive attitude to the migration of talent that sustains our universities. Similarly, on the rights of EU citizens residents in the UK, I think that I have said before in this forum just how difficult it is at the moment for university leaders who so often are approached by staff from EU nations who have been resident in Scotland often for a long time. We are saying, look, I do not know what my family's entitlements are going to be in future, not just to stay, but to access public services. I am going to still be able to use the health service on the same basis as a UK citizen, what happens to my kids going to school and so on. I think that the Prime Minister did say something useful in saying that she wanted to guarantee the rights of EU citizens who are already living in Britain. I would like to see that concretised. What does that mean in terms of rights not just to stay, but to access public services? What will that mean in terms of our ability to attract future staff from the EU? That is a problem that universities are already facing when you are running a competition to get the best possible staff for a role, staff from the EU, and I do not think very seriously about whether they actually take up an offer from a university in the UK, and certainly anecdotal evidence is some of her saying, I just do not know enough about what my entitlements would be to make that choice on behalf of myself and my family. A third element where I think there was a hint of going in the right direction that again needs to be followed through was on research collaboration with the EU. I think that I have said again in this forum that arises in 2020, and not just the money, but particularly the sustaining of relationships of collaboration with our neighbours has been really important for the excellence of universities in Scotland. I think that the Prime Minister did give an indication that she was open to an agreement to continue to collaborate with her European partners on science and research and technology. Again, I think that one would want to see that built on in a concrete way. Does that mean that potentially the UK Government is prepared to buy into horizon 2020 and to support that real density of academic collaboration that exists across the EU? Good. Richard Lockhead, do you want to come in there? Thank you to everyone for coming to give evidence. I guess that one of the themes that I am keen to explore is where Scotland stands in terms of soft Brexit versus hard Brexit. As some people have indicated, we may well be on the way to leaving the single market, which is hard Brexit, unless Scotland is able to negotiate something bespoke to our own needs. In terms of the people around the table from my glean of the debate, the most representative of leave camp in Scotland, the 38 per cent would be the farmers and fishermen. About two thirds, if not three quarters, of the farmers that I have spoken to since EU referendum voted to leave. Virtually every single member of the catching sector of the fishing industry I have heard speak of the subject as back to leave in the EU referendum as well. If it is your view that those who voted to leave would have preferred a soft Brexit as opposed to a hard Brexit in terms of your members.  Obviously, our industry is heavily supported by support from the EU, but also in terms of the trade, as I touched on my opening remarks. As you have said, the industry was fairly split on the issue. A lot of it came down to the rules and regulations. They felt that their hands were tied by red tape and that if we were outside the EU, we could possibly build a more outward looking future for ourselves, I suppose. On the hard and soft Brexit, it is a difficult question to answer, because I think that we really need to have much more detail of what each option would look like. If we are referring to soft, then that might be remaining within the EU single market. If Scotland is to remain in, but the rest of the UK is to come out, where does that leave us in terms of cross-border trade? On the hard Brexit, again, as I touched on in my opening remarks, it entirely depends on the sort of free trade agreements that we will be looking at in the future and whether or not we will still be able to sell our produce to not just an EU market but an international market as well. What I will say is that I think that it would be naive for the industry to assume that if we are coming out of the single market, we will be able to build a brand new shiny system free of all the rules and regulations that farmers can often complain about. The EU will still remain a significant trading partner, and it is slightly that we will have to have some element of regulatory alignment with that, with whatever system we build for ourselves, and likewise we will be constrained to some extent by the likes of World Trade Organization rules. We need a better idea from Government. We have a little bit from the Prime Minister now as to what she sees the future looking like, but we need much more detail about how that will impact on our different sectors. I suppose that I might be unique in that room. In a sense, as Mr Lockhead had said, our industry has been very clear that we see that there is a huge opportunity to leave Europe for our industry on a number of fronts. One of them has been the release of our industry from the common fisheries policy, which has been as far as we are concerned a very centralised management system, which has played its part in the demise of similar coastal communities. Certainly, in relation to things such as our fishing opportunity or our quotas, it is a mind boggling system altogether. I have certainly sat through, I think, close to 20 years of December fisheries councils, ten with Richard Lockhead, two years when he was shadow minister and eight when he was minister. We would sit in the building, Scotland's building and Brussels in Scotland House, and continually say that there must be a better way to manage fisheries than that. I think that it is probably the Parliament's in agreement with that. We really see that there is an opportunity to have a better system of management in place. Certainly on two fronts, A, sustainability for stocks, and B, the economic profitability of the sector, the entire sector. The other main issue in terms of the hard or soft Brexit, of course, is the market. Us as a sector, we certainly need a market. We are largely exporting. The whole market is very important, but the international market is important. Post-Brexit, we definitely need a trade deal that we can trade with both EU, but we also see there are huge opportunities to trade with other importing and exporting nations across the world. Naturally, the continued tariff-free access to the European market is our preferred option. That is our preferred option. In the event that this is no longer possible, we could see that there would be a huge benefit, not only from the UK but from the EU as well, to have a system where we have a mutual beneficial trade relationship that involves low-impact tariffs and also tariff-free quotas. That is definitely our option, but we do see that there are opportunities, even outside the customs union, to access other markets, especially for fish that we can freeze. Places such as India and Turkey spring to mind straight away that there are big populations there. That could be a huge demand for our Scottish produce. There are opportunities there, but I will say this—this is our huge caveat—that we see in terms of Brexit that the key issue is access to our resource. We do not want to see a situation where access to the single market is traded against getting access to our fishery zone. It is absolutely key to our success in terms of post-Brexit. What does that mean? It means that day one after Brexit that we are in control of who is coming into our waters and how much fish they are catching. That is absolutely key to the future prosperity of this industry. We know at this particular time—I will finish on this one—that of the European Union catch, including the UK waters, 60 per cent of the catch is taken by non-UK vessels. We do not see that that is a system that is right or proper for an industry that would be a coastal state. We need to rebalance that situation. Tavish Scott, did you want to come in on that point? Can I ask a supplementary question to both Gary and Ian? If we could maybe stay with fishing for the moment, because I think Richard wants to come back in. The Prime Minister made a specific mention in her speech last a week past Tuesday of Spanish fishermen. She did not go unnoticed among the fishermen of Shetland that she mentioned Spanish fishermen. She certainly did not mention Scottish English or Welsh or for that matter not an Irish fisherman. I was wondering if Ian Gatt has a reflection on that in the context of your last observation about what could be traded away given what has happened in the past. That is our clear fear that we are used as a bargaining chip to secure other things. We will only have the vision of profitability and rejuvenising our coastal communities if we are in control of our own destiny. That was certainly a fear. What the Prime Minister said was not clear at all on what she meant by the Spanish fisherman, and we are actively seeking some clarification on it. It is clearly a worry. I was in a similar vein. I would not ever criticise any fisherman in the catching sector for voting Brexit for the purposes of community common fisheries policy. What is your message to the Prime Minister, given what she said in her speech, which seemed quite clear to me, was that the reason why she is confident of being able to, in her view, get a good trade deal to the EU is that countries such as Spain will want to negotiate continued access for Spanish fishermen into Scottish waters. What is your message to the Prime Minister? You are right that that is a particular fear in the sense that we would be used as a bargaining chip. We are absolutely clear in our position that the market should not be traded against us having control of access to our fisheries. It is absolutely key, because if we have not got that, there is no way that we can go forward with the vision that we have. There is a sea of opportunity. We cannot be in it. We are promoting that we can build the coastal communities that may back up to where they were before. It is absolutely key. Access is key for us. That is a supplementary one. Just on the point regarding trade and fishing. For the UK to seek a good deal, or as best a deal as possible, there will be other wider implications and other issues that the EU nation states will certainly want to put on the table. Particularly when it comes to established scot highlighted regarding Spanish fishermen, there may be some issues that concern Spanish. In order for some type of deal to be done in the fishing sector and access to waters in Scotland, it could certainly be part of that. In terms of yourselves as an organisation, is that something that you have been fully considered? We are fully considered. We think that the balance comes down on ensuring that we have control over our access rather than trading away with the market. Yes, the market is hugely important, but one of the things that is forgotten in the debate is that, of course, Europe will want to trade with the UK. There is a mutual beneficial interest in trying to get a trading deal that suits us both. On the balance of it, we see that the most important thing is getting back control of our resource. To follow that and completely understand the point about resource being the top priority for the fishing sector, what is the current state of play in terms of the market? What share of produce from Scotland or Scottish catching goes to the European Union out with the UK? What share goes to markets beyond the European Union? I think that there is no doubt that the majority of the fish that we are exporting is going into the European Union. Last year, it was around £450 million of our sales. Yes, it is important, but we are not so pessimistic as maybe a lot of people are in terms of trying to strike this trade deal, because we think that it is in the European Union's interest as well to trade with Scotland. As I said, our principal point is that we do not want to see the market traded against access to our resource. I know that there are a number of other members wishing to come in. Can we restrict it to fishing for the moment? Emma Harper, did you have a question about fishing? No, Mike, it's clear to me. No, Mike, it's clear to me. It was Ross who was your question about fishing. Can I just also make the point that a number of members of the committee have just come back from a visit to Brussels, where we had extensive conversations with the MEPs and the experts and other organisations? What came across strongly was that the Spanish are very concerned about Gibraltar, and we are regaining sovereignty to Gibraltar. That will emerge as a key issue in the negotiations. In return for giving up Gibraltar, they will drive a hard bargain. Would you be concerned that access to Scottish fishing grounds and UK fishing grounds would be an aspect of that? Is that being raised? Is the specific subject being raised with you about Gibraltar as well? No, it hasn't. It's an interesting point that you make. I'm sure that people across the European Union, especially in the fishing community, because although it seems that we are wide and diverse, we do meet our European colleagues. We know that they are working actively on strands of argumentation that they can put forward to ensure that they maintain the present access arrangements that they have. It doesn't surprise me, but, as I said, we see for Scotland that there is a huge opportunity to grow this industry, a huge opportunity, and I think that we should grasp it. Thank you. Emma Harper. Thank you, convener. Good morning, everybody. My question specifically about farming NFU. NFU is going through elections now for our new president and vice president, and that's obviously putting another spanner in the Brexit works. My questions are around the red tape that you talked about and what are the difficulties that the farmers are seeing, but when I speak to farmers on the ground, some of them are genuinely excited about Brexit and the opportunities, but others are really concerned about the potential of 42 per cent tariffs on dairy products or higher tariffs on beef and sheep. I mean, our farmers, whether they are Highland or in the south of Scotland where I am from, are dairy. Should they really be concerned about this hard Brexit, soft Brexit? I mean, I'm curious as to why they are really excited about it. As I said in my previous remarks, different trade scenarios will have different impacts for different sectors of the agricultural industry, so as much as our response to the Brexit scenario today has been a Scottish agriculture PLC response, what we are trying to do at the moment is to get a much better understanding of the impact of various different potentials of tariffs and also non-tariff barriers for different sectors of the agricultural industry, because what might be quite useful for one sector, perhaps the dairy industry in terms of outward exports, might be extremely dangerous for others like the livestock guys. We're in the process of gathering much better information on the likely trade scenarios and the impact that I'll have, and then putting that to our membership to say what is it that we should be pushing here. I mean, as I've said, what would be desirable is something, if we could possibly emulate something similar to what we have at the moment in terms of the balance of trade. We're currently, the UK is a net importer at the moment, so perhaps there could be a better redress done there in terms of our self-sufficiency, but it's a hugely complex area, and as I said in my remarks to the previous question, if it is free trade agreements that we're looking at, there are serious concerns about our capability to negotiate a deal that is going to suit all sectors of the agriculture industry within the two-year timeframe on a bilateral basis, it does seem like a serious challenge ahead. Many of the organisations, if not all the organisations around the table, welcomed to one extent or the other the Scottish Government's proposals, the Scotland's place in Europe paper. I was wondering if, off the back of the Prime Minister's speech, if you had any further thoughts on the Scottish Government's proposals and how compatible they are with the position that the UK Government has now outlined. We did welcome the Scottish Government's piece of work and I think it was, at the time, it was the only piece of work that had been done that I had really looked in any detail about what a future solution could or might look like. I think to be clear, we welcomed the fact that the piece of work had been done. We didn't necessarily welcome what the proposals were because we hadn't got there in our policy or in our thinking yet. Now we've heard from the Prime Minister and I think that that does raise quite significant challenges potentially around how you would marry the Prime Minister's vision and the Scottish Government's vision together. One of the things that the paper said quite clearly was the idea that, if Scotland maintained its single market access, it would do so while maintaining its access in the UK market. From our point of view, as Tragedonists, we don't have a defined policy about what we want to see going forward but we do have priorities. We want to defend workers' rights, we want to defend social protections, we want to defend jobs through market access and make sure that our employers can trade freely within the markets that they see as priorities. We also want to make gains where possible. We want to see a better industrial strategy, we want to see state aid being able to be given to industries, things that are currently prevented by European rules. We would like to see the living wage promoted through procurement, those sorts of things. We would like to look at where we can actually make gains in that area, but the question for us would be, how do you ensure that those priorities are met, whether it is through the UK Government's proposals or the Scottish Government's proposals? There are significant challenges in the paper around how you would ensure the different market access, for example. We would want to be sure about the choices that we were making and we would not want to see any unintended consequences for industries in which we have members. I think that there is quite a lot of thinking that needs to be done around that and it is something that we will be looking at more in the future. Are there any other witnesses that would like to come in at that point? Yes, Marina. We did also welcome the fact that the Scottish Government produced a paper. It is important to start looking in detail at what it is that is going to be debated. We are taking the Scottish Government's paper and its clear preference to remain within the single market. We are looking at the Prime Minister and her speech stating clearly that that was not the UK Government's position. That is obviously going to bring up some challenges, but the fact of the matter is that the range of possible outcomes is still extremely wide and there are a lot of issues that we need to look at within that. Whatever the ultimate framework ends up being for Scotland and the UK and their relationships with the EU, we need to take into consideration how we are going to protect citizens' rights and how we are going to make sure that everyone is able to enjoy certainty in the law and stability. That can be done in a lot of different ways, but we need to start listening and hearing what both sides are going to be debating in the weeks coming forward. Marina, can I just follow up on that? One of the things that the Prime Minister was very specific about was leaving the European Court of Justice. Again, when we were in Europe, what came across very strongly was that in the people that we spoke to, any free trade agreement or any kind of access to the market would require the UK to sign up to a regulatory framework and there would have to be an arbiter to that. There is a big question mark over what the arbiter is going to be and there is no European Court of Justice to arbitrate those things. What is the law society's view on that? You are right that the Prime Minister did specifically say that the Court of Justice wasn't something that we wanted to take part in any more. What terms are going to be agreed for any deal that comes forward is a matter for political negotiation and we will have to wait and see what comes forward. We do have some concerns at the law society about what is going to happen to current pending cases, so people that already have cases going forward that are on route to going to the Court of Justice at the moment or in the future might end up with a referral that way. We have looked at a couple of different ideas for how you could make sure that those people still were able to access decisions and resolve their cases, but it is something that we need to look into further. Thank you. I am aware that we have not heard from Gary Clark yet. I do not know if you are being pretty particularly shy this morning. No, I am happy to contribute. It is an interesting discussion. I have to say from the point of view of our members that they are probably less interested with the greatest of respect than what the politicians are saying than their own priorities being met and how the politicians respond positively to that. In common with others this morning, one of the clear priorities of our members in relation to the EU is to ensure continued tariff-free access to the single market. There is also a desire to ensure that we have an adequate supply of labour from international marketplaces. Clearly remaining within the single market would have been an obvious way of addressing those issues, but that is not to say that they cannot be addressed from outside of that, as others have already mentioned. We want to see a clear deal to ensure that tariff-free access to the single market is possible. We want to see clear guarantees in terms of the rights of EU citizens already here to work here, but we also want to see an expansion of the ability of people from the EU and elsewhere to come to Scotland to work and to take part in our economy, because we believe that that is a clear economic need. Whether you are approaching that from the point of view of free movement or you are approaching it from the point of view of managed immigration, then there is a clear economic need within Scotland to ensure that we have those people coming to our country, to study in our universities or to work in our businesses. From that point of view, those are the clear priorities of our members that they have stated to us. I met a range of members from a variety of sectors just the other week. They did not want to talk about the politics of Brexit. They were fed up with it. However, what they did want to talk about was how they realised their aspirations that they need to ensure that their businesses can continue to operate in the way that they have been doing and to explore new opportunities. Lewis MacDonald That is very interesting. I think that I have heard from a number of witnesses objectives that are all completely understandable and desirable but potentially in contradicting with each other. To Helen Martin's point about procurement and state aid was a very important point. When we were in Brussels, we met Esther Lynch from the European TEC who talked about the work that had been done to change the social clauses in relation to public procurement, to allow public procurement to have such clauses and also reforms that were being pursued in relation to the Post-it Workers Directive, again to allow trade unions to have a more active say in those matters on a national basis, as well as across the United States as a whole. I guess that my concern, or what I would be interested to hear people's views on, is how—we have talked about access to the single market from a business point of view or from our farming and seafood point of view—that is clearly important. What mechanisms are your organisations considering in terms of future influence on policy within Europe? Clearly, as members of the single market, even as members of the single market outwith the European Union, there is not that direct role of influencing policy. What else is available to influence policy in ways that will clearly affect this country, whether we are outside the single market or seeking to negotiate a free trade arrangement? That is one of our key issues. We were a Romanian organisation. We really wanted to see the UK Romanian within the European Union, but we were not a Romanian organisation with no caveats. We were a Romanian in reform. It was a very key part of our position that we thought that being a member of the European Union gave us the most ability to reform the European project, to bring in the social dimensions, to do the sorts of things that Mr MacDonald has just outlined in terms of changing procurement regulation and post-workers directive. That is a key part of why we thought that it was so essential that the UK maintained its membership. One of the things that we will be thinking about going forward is what the other options give you in terms of influence. The Scottish Government's paper talks about F, the membership for the UK and potentially for Scotland. We have done some fact-finding with the Norwegian trade unions and the F, the co-ordinating committee that does the social dialogue. We have talked about what the influence looks like and how you influence the decisions that are coming down from the European Union. We received very clear indication from everyone that these are not influencing opportunities, that there is no influence. I have never heard so many people tell me so clearly that they have no influence over the rules that govern their lives. I think that for us that would be something that we would really need to think about whether it was acceptable to have no influence over the decisions that are being made and the policies that are being taken. As trade unionists, we will always, to a certain extent, have influence because we will always have our trade union structures. We will have the ATUC. We will be able to work together across Europe, across internationally in the way that we do. Those structures are not related to the European Union. They will not be torn down, regardless of what we do in terms of our European membership. In some ways, we are trying to strengthen our arrangements from the SUC to the ATUC and to other key trade union centres in Europe in preparation for those negotiations. I will follow up on that point, because in terms of the UK Government's proposal that is not after us, it is outside again. We have been told in Brussels that if you want to sell into the market, you have to abide by the rules of the regulations, otherwise you do not sell into the market. You are talking about if it is not satisfactory, and it is fair to say that we have taken evidence on that as well, but then being outside completely, you have no influence at all either, but you still have to abide by the rules if you want to sell. I think that this is a point that we absolutely recognise. In some ways, Europe does not go away. It just does not. That is why we were a remaining organisation. We still, to a certain extent, think that the best option is to be a European Union member. It does feel a little bit like that ship has sailed, however. In terms of the negotiations with the EU, it is clear that we are going to have to negotiate some form of relationship and trade deal. For us, it would be good to have a clear understanding of what regulation is going to apply, and we would hope to see a lot of social regulation still applying at the end. We would like to see the European Court of Justice still having a role to play here in the UK. That is something that has provided good findings for in defence of workers' rights. Those are priorities that are potentially quite difficult to achieve. We recognise how many questions will need to be resolved going forward. As I said, those are all questions that we will have to debate within our own movement and bottom out, but we have a range of priorities and we are hoping to see those achieved in the future. Thank you very much. Stuart McMillan, you wanted to comment. On this aspect, in recent weeks or months, one example that has been provided has been the automotive sector. The discussions are the potential for a preferential deal for that particular sector. You are all here representing your various organisations and you are pushing your own individual cases, but if, at some point, a deal is undertaken, bear in mind that it will be a transition deal first and then the final deal, but by the time we get to the end of a process, whenever that is going to be, there will probably be someone else and some losers. What are your opinions and what discussions are taking place within your organisations? To A, make sure that you push in the strongest possible terms at your own particular sector, but secondly, if your sector ends up being one of those that is not one of the winners, what discussions have taken place thus far within your organisations on that tick off scenario? Just on that point, in your Scotland, you have made it quite clear that, as representing 500,000 students across Scotland, it would be detrimental if we are going to be losing out on some of the funding that comes directly from the EU, and Alasdair was saying the same. I just want to highlight that that does not only affect universities, it affects a lot of our colleges as well. If any of the negotiations are not going to be benefiting the students and the future of our country, that would be detrimental. There would almost be no benefactor to that. Especially as Theresa May, in her speech, says that she wants the UK to be at the forefront of research and education. How are we going to do that without the lack of funding that will come following a leave of the EU? I guess that that is not an answer to your question, because there is almost no answer to that. We have no structures in place, and there are no guarantees in place for the students and for the universities and colleges in terms of getting that funding. In responding to your point about channels of influence, one of the important things for us is that this Parliament's voice is a clear voice and a voice that is heard. Across this party, we have had consistent support for making sure that we are able to attract student talent, staff talent from across the European Union and beyond, and that we are able to continue to collaborate in research networks that help to make Scotland such an absolutely excellent place in terms of brilliant and impactful research. If we can have that voice consistently and still on this cross-party basis from Scotland, I believe that that should have some force in the UK's overall consideration of its priorities. We, as the University of Scotland, work with our affiliate organisation Universities UK, which is getting very similar messages to the UK Government. I hope that, to some extent, that is what we have seen reflected in the Prime Minister's speech. There are two tracks of influence there, but I really think that the extraordinary cross-party consensus that we have about ensuring that Scotland's universities are open to the world is an important part of the weight of that argument. I know that Gary wants to come in, but, obviously, universities throughout the UK are really important. Is it fair to say that, in terms of the shape and size of our economy, that universities in Scotland are an even more important sector proportionally than in the rest of the UK? I think that that is right. I think that there are a couple of sectors that are bigger than financial services and oil and gas are bigger in terms of economic impact, but there is not much more beyond that. It is bigger in terms of economic impact than the scale of our university sector, with getting on to 40,000 direct employees, an indirect employment effect of about 150,000. Looking at city regions like Dundee, a very large percentage of employment is traceable back to having really powerful and excellent universities. Overall, economic impact is a bit over £7 billion in terms of the economic advice that we have had. That has been recognised on a really robust cross-party basis here, and I think that that really should carry weight. I just wanted to come back to the issue of, obviously, the cases being made in terms of a special deal for the automotive industry. I hope that it is not about winners and losers in this, I hope that it is about making sure that each sector, and we represent a wide range of sectors, gets treated appropriately. Certainly, in terms of the automotive sector, in terms of the aerospace industry, there is so much that is done on a cross-border basis at the moment that I think is absolutely essential for the smooth operation of those industries, that they do form some sort of, whether it is some form of remaining within the customs union or whatever, to ensure that they can continue to operate the way that they operate at the moment. I think that that is in the UK's interest, and I think that it is in the interests of businesses in other member states as well. It is about getting the most appropriate solution, and I say for most of our members that it is about making sure that tariff barriers are as low as possible, because that would be the defining factor in terms of whether a business is able to retain its margins or struggle. As one senior politician in Europe said to us during a negotiation, if you want something, you have to be prepared to concede something in order to get it. I was just going to come back to Gary Clark, because in a way it feeds back to my previous question that Helen Martin answered very fully, but clearly a concern for business must be not just tariffs but also non-tariff barriers and the requirement to comply with European standards, and particularly given that none of the solutions on the table offer access to the setting of those standards. I wonder what business feels about how you can influence standard setting or customs requirements if we are out with the European customs union. I think that there is a long way to go on this. I mean, certainly speaking to members, I mean, they are currently operating within those existing standards. I mean, there are even difficulties sometimes even within the single market in some aspects of that, but they are currently operating within that and they are familiar with that. Many have expressed to us the optimism that, hopefully, if we are currently familiar and engaged in meeting those standards, even if we are outside the single market, at least in the first instance, we would have a better chance of achieving a trade deal and continuing to work within those standards. The difficulty would then come if standards changed. Obviously, we would need to look at the flexibility within any agreement that we came to with the EU single market to be able to reflect that and for our own national legislation and regulation to reflect that as well in the longer term. I think that that is what I am keen to understand because, on day one, the standards are identical, but on day two, they begin to diverge. Do you think that that needs to be part of a free trade agreement? How do you envisage avoiding that becoming a situation? I think that any agreement that the UK came to in terms of access to the single market would need to cover that kind of detail. As others have said, it will take a significant amount of time to do that. It is important that we do it and that we have robust transitional arrangements to allow us to not lose out over any future agreement. Do you think that there is an understanding that there is not going to be a deal within two years? It is a difficult question. We are representing businesses of many different sizes. Many businesses are realistic in terms of their expectations, particularly if they have engaged at a European level before. They know the glacial pace at which things operate, not just on a European basis but on an international basis. There is that expectation among some businesses. Other businesses may have different expectations, and that is why we need to ensure that we do not get the right deal at the end of the day but that we have a flexible transitional arrangement whereby businesses do not lose out. We cannot afford to lose businesses along the way to reaching a formal trade agreement with the EU. It is fair to say that, in Europe, the politicians we spoke to are very clear that the free trade discussions happen after the two years after the exit deal has been completed. In terms of the Prime Minister's speech, did you feel that what she said about transitional arrangements was robust enough? In terms of the Prime Minister's speech, again, not wanting to get drawn into the politics that our members are frustrated with, but what it tells us is more about the starting point of where we are. It does not tell us any more about the end point. From that point of view, we are still lacking clarity. We do not know where we are going to end up. We know what our priorities are and we will continue to reinforce those with the Scottish Government, the UK Government, our colleagues in chambers of commerce, not just in the rest of the UK but in chambers of commerce and, of course, Europe as well. In terms of the Prime Minister's speech, we know a bit more about the starting point, but we know absolutely nothing more about the end point. I was going to ask a wider question to other witnesses as well, about transitional arrangements. Did any other witnesses have anything to say about transitional arrangements? The particular thing was the discussion when we were in Brussels. We had a very full discussion with the law societies of the UK around the possibilities on transitional arrangements, which included that WTO rules would allow a transitional arrangement to last for as long as 10 years. That seemed to mirror what people were saying was the likely time that it would take to negotiate a final outcome. I just wondered from the law side of Scotland or from others, with a close interest in that question, what the view is of potential transitional arrangements. As Gary Clark said, we start from a position where we comply entirely with all European requirements. We do not know where we are going to be 10 years down the road, but is it the view of the law society that those transitional arrangements could maintain quite a lot of those existing standards and requirements over quite a large part of that 10-year period? I think that you are right that the WTO rules say that you can have up to 10 years to get these things settled. Realistically, whether any of the parties involved are going to be happy with a 10-year long transition is going to remain to be seen. There are a lot of complicated issues to be dealt with during a transition and the Prime Minister, I believe, was talking about a phase transition, so dealing with different parts at different times, but the ultimate timescales for that will be dependent on all of the many countries involved in agreeing with this. I think that it's fair to say that I didn't pick up a great deal of enthusiasm for that option when I was in Brussels. Did you want to come back in, Fiona Ross? No? No? Ross Crew? I would like to ask Fiona Hidie specifically about representation of your organisations and the large demographics, large groups of people that you represent. I know that the youth parliament had lobbied to have representation on the standing council, but now that we are entering the next phase, negotiations will start in a few months. What expectation do you have of how you will be engaged in that process? I will start with that. I think that it's something that we have to consider very seriously, and I would urge the committee to bring into its considerations, because whilst there are a number of organisations representing very important sectors of Scotland, I'm here representing a generation of Scotland. That comes with a lot of problems. There's a lot of different voices, with a lot of different opinions, but they really, really do have to be listened to. I think that we're definitely back together with the suggestion that I know that they've submitted to the committee that an expert on child and young people's rights be appointed to the advisory panel. We definitely seek further engagement with that committee, which I really thank for having us here today. I would seek further engagement, perhaps bringing other young people in as well, to work directly with the committee. It would be a fantastic way for you to get a sense of the diversity of voices out there. Thank you for that question, Ross. Again, I just really want to reiterate what Fiona just said, that we're very pleased to be sat here at the table and to be able to reflect our experiences. In terms of the diversity of the people that we're representing, I'm sitting here as a European student. I came here five years ago, and I'm not planning on leaving unless I'm being kicked out. For us to have the opportunity to sit at the table and reflect that and make sure that that's heard, it's a vital opportunity for us, and we would be very pleased to be invited back. I think that we've made some of our points quite clear in some of the statements that we've released as well, and we won't stop pushing that either, and we will continue. So we'd be quite happy to be invited back and we'd be quite happy to answer any questions specifically for students, and also to remember that not all students are young people either, so we will have generations that are not reflected just from the Scottish youth Parliament as well. Thank you. Thank you very much, and we're very grateful that you're here today, and I know that the committee does have plans and has been discussing plans for further engagement with young people, so thank you and thank you to the rest of our witnesses who've come here today. I'll now close the public session of the meeting.


It was a bit slow and I started not so good, had a good practice yesterday and went with what I thought was best and let me change the ball after the third heat, it seemed to be a bit better but still lacking the speed, made some change for the last one and I found something good so shame I found it in the last heat and not in the first one because I had plenty of speed in the last one so yeah it's a shame but at least we got a win and yeah you're only as good as your last eight. It's beginning is was so hard you know and then after a second heat I changed the bike and it was like different story and I feel it's good speed is my bike is pulling you know from the gate and from the out of the corner so I think you know it's I need to be happy because you know it's like I said you know it's beginning is was to zero and and then later we we catch good points and we'll see you know we we hard work and I just want to say you know it's thanks to my team and they're working today it's really hard and that's that's good tough night I still managed to get ten points but a batik is catching me now in it overall standing so yeah it was not so good I I had I had terrible starts tonight so made my life more more difficult when you when you can start so I made a good good one in the last in the semi final but I was lifting too much and got out of control so that was my own mistake yeah you know still ten points in the bank and we're still in the in the game for the championship but it's a it's getting tight now in the left for the last three rounds I'm happy because I'm get to second place and not so no bad results for me for my team and but behind me so three runs very hard and and I was a boy in scar diff and tournament I'm looking looking and only for the for for the three runs and yes I love it's beautiful and I waiting for the racing