Question 26.32: Simplify the circuit of Fig. 26.55 (i).

The Boolean expression for the circuit shown in Fig. 26.55 (i) is

$X=(\bar{A}+B)(A+\bar{B})$

Step 1. Multiplying out to get the sum-of-products form, we have,

$X=\bar{A} A+\bar{A} \bar{B}+B A+B \bar{B}$

Step 2. Now $\bar{A} A=0 \text { and } B \bar{B}=0$ so that :

$X=\bar{A} \bar{B}+A B$

This expression is implemented in Fig. 26.55 (ii). If you compare the circuit with the original circuit, you see that both circuits contain the same number of gates and connections. Therefore, the simplification process has not produced a simpler circuit but it has produced an alternative circuit.