Minecraft wiki entry for Calculator, associated text: Here is how to construct a multiplier, in order from the least to the most significant bits.
Least significant bits : 1*1 = 1. That means that the output of the second AND gate (the control one) goes straight to the output collective wires.
Second to last: 1*2 = 2 and 2*1 = 2. Those two outputs meet in a full adder. The sum goes to the output, and the carry goes to the next bit.
Next: 1*4 = 4; 2*2 = 4; and 4*1 = 4 The carry from the last bit goes in the first adder as the carry input. The two normal inputs are 2 of the 3 AND gates. The sum of this goes in a second adder, where the second input is the third AND gate. Both carry outs go to the next stage, and the sum goes to the output.