Question

In the following circuit all are 4 $\times$ 1 multiplexer. The output f is

• A. $\overline{W}X\overline{Y}\overline{Z}+W\overline{X}\overline{Y}\overline{Z}+XY+YZ$
• B. $W\overline{X}YZ+\overline{W}XYZ+\overline{X}\overline{Y}+\overline{Y}\overline{Z}$
• C. $W\overline{X}\overline{Y}\overline{Z}+\overline{W}\overline{X}\overline{Y}Z+Y\overline{Z}+ZX$
• D. $\overline{W}XYZ+WXY\overline{Z}+YZ+\overline{Z}\overline{X}$

Answer 1

The correct option is A $\overline{W}X\overline{Y}\overline{Z}+W\overline{X}\overline{Y}\overline{Z}+XY+YZ$

Let the output from the upper first level multiplexer is $f_a$, and from the lower first level multiplexer is $f_b$

$f_a=\overline{W}X+W\overline{X}$

$f_b=\overline{W}X+WX=X$

$f=f_a\overline{Y}\overline{Z}+f_{b}Y\overline{Z}+YZ$

$=(\overline{W}X+W\overline{X})\overline{Y}\overline{Z}+XY\overline{Z}+YZ$

$=\overline{W}X\overline{Y}\overline{Z}+W\overline{X}\overline{Y}\overline{Z}+XY+YZ$