An inverter in RTL has designed the combinational circuit shown below. His…
2026
An inverter in RTL has designed the combinational circuit shown below. His supervisor is unable to comprehend its functionality and has sought your assistance in this image:
Circuit description from the image:
Inputs: A, B, C
Upper gates: B AND NOT C
Lower gate: B XOR C
These two outputs go to a 2:1 multiplexer
A is the select input of the multiplexer
Output is F(A, B, C)
A | B | C | F(A, B, C) |
|---|---|---|---|
0 | 0 | 0 | |
0 | 0 | 1 | |
0 | 1 | 0 | |
0 | 1 | 1 | |
1 | 0 | 0 | |
1 | 0 | 1 | |
1 | 1 | 0 | |
1 | 1 | 1 |
(a) Fill in the truth table for F(A, B, C) above and express F(A, B, C) in minimal sum-of-products form.
(b) Is the function F(A, B, C) universal? If so, construct the corresponding circuit with precise input combinations and determine the resulting output.
Attempted by 2 students.
Show answer & explanation
(a) Truth Table and Minimal SOP Form
Truth Table Values for F(A, B, C):
The multiplexer logic is defined as: F = A'(B . C') + A(B ⊕ C).
For A = 0, 0, 0: F = 0
For A = 0, 0, 1: F = 0
For A = 0, 1, 0: F = 1
For A = 0, 1, 1: F = 0
For A = 1, 0, 0: F = 0
For A = 1, 0, 1: F = 1
For A = 1, 1, 0: F = 1
For A = 1, 1, 1: F = 0
Minimal Sum-of-Products (SOP) Form:
Taking the minterms where F = 1:
F = A'BC' + AB'C + ABC'
Using a Karnaugh map or Boolean algebra simplification:
F = BC' + AB'C
(b) Is the function F(A, B, C) universal?
A universal function/gate must be capable of implementing all Boolean operations.
Universal realization generally requires NAND or NOR functionality.
The given function:
F(A,B,C)=BC′+AB′C
cannot independently realize all Boolean functions.
Hence, it is not universal.
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