 Since formula_12 and formula_13 are bits, formula_20 if and only if formula_21 and formula_22.An important point worth mentioning is that the half subtractor diagram aside implements formula_23 and not formula_24 since formula_15 on the diagram is given by
This is an important distinction to make since subtraction itself is not commutative, but the difference bit formula_14 is calculated using an XOR gate which is commutative.The truth table for the half subtractor is