Question 16.11: Write the Boolean expression and truth table for the logic g......
Write the Boolean expression and truth table for the logic gate circuit shown in Fig. 16.8.
The Boolean expression is developed as shown below.
The Boolean expression is
\begin{aligned} \mathrm{X} & =\overline{\mathrm{A}} \cdot \overline{\mathrm{B}}+\overline{\overline{\mathrm{A}}+\mathrm{B}} \\ & =\mathrm{Y}+\mathrm{Z} \end{aligned}where \mathrm{Y}=\overline{\mathrm{A}} \cdot \overline{\mathrm{B}}
and \mathrm{Z}=\overline{\overline{\mathrm{A}}+\mathrm{B}}
Now let us write the truth table. We first write the various combinations of 0 and 1 for the two inputs, A and B. There are 2^N = 2^2 = 4 combinations. For each row of inputs, we will calculate Y and Z, respectively. Then we would add Y and Z, to get X.
Truth table
\begin{array}{|ccccc|} \hline \mathrm{A} & \mathrm{B} & \mathrm{Y} & \mathrm{Z} & \mathrm{X} \\ \hline 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 \\ 1 & 1 & 0 & 0 & 0 \\ \hline \end{array}
