Question

A logic circuit implements the Boolean function, $F=\overline{X}Y+X\overline{Y}\overline{Z}.$ It is found that the input combination $X=Y=1$ can never occur. Taking this into account, a simplified expression for F is given by

Answer 1

$F=\overline{X}Y+X\overline{Y}\overline{Z}=\overline{X}Y(Z+\overline{Z})+X\overline{Y}\overline{Z}$
$=\overline{X}YZ+\overline{X}Y\overline{Z}+X\overline{Y}\overline{Z}$
Truth table:

$$\begin{array}{cccc}X& Y& Z& F\\ 0& 0& 0& 0\\ 0& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 1& 1& 1\\ 1& 0& 0& 1\\ 1& 0& 1& 0\\ 1& 1& 0& \times \\ 1& 1& 1& \times \end{array}$$