In the circuit shown, ๐ and ๐ are MSBs of the control inputs. T
In the circuit shown, ๐ and ๐ are MSBs of the control inputs. The output ๐น is given by
A. F = WXฬ + Wฬ X + Yฬ Zฬ
B. F = WXฬ + Wฬ X + Yฬ Z
C. F = WXฬ Yฬ + Wฬ XYฬ
D. F = (Wฬ + Xฬ ) Xฬ Zฬ
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
For a general 4 to 1 multiplier as shown, the output expression is written as:
F = Sฬ 1Sฬ 0I0 + Sฬ 1S0I1 + S1Sฬ 0I2 + S1S0I3
i.e. I0 will be the output when the select inputs are 00, I1 will be the output when the select Inputs are 01, and so on.
Analysis:
The output of the first MUX is given by:
\(Q = \overline {WX} {I_0} + \bar WX{I_2} + W{\overline {XI} _2} + WX{I_3}\)
With I0 = I3 = 0, and
I1 = I2 = 1
\(Q = \bar WX + W\bar X\)
Similarly, the output of the second MUX is given by:
F = Yฬ Zฬ Q + Yฬ Z Q + 0 + 0
F = Yฬ Zฬ (Wฬ X + WXฬ ) + Yฬ Z (Wฬ X + WXฬ )
F = Yฬ (Wฬ X + WXฬ )(Z + Zฬ )
F = Yฬ Wฬ X + Yฬ W Xฬ
