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The combinational logic circuit shown in given figure has an output Q which is—
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- ABC
- A + B + C
- A ⊕ B ⊕ C
- A ⊙ B ⊙ C
Correct Option: B
Output of MUX, Q = A BC + AB + AB + AB
Multiply by (C + C) the term which contain no C term:
∴ C + C=1
Q = A BC + AB (C + C) + AB (C + C) + ABC (C + C)
or Q = A BC + ABC + ABC + ABC + AB C + ABC + AB C
This can be simplified by K-map, from K-map
Q = A + B + C
Hence alternative (B) is the correct answer.
Alternative Method:
Output of Mux, Q = A BC + AB + AB + AB
or
Q = A (BC + B) + A (B+ B)
or
Q = A (B + C) + A {∵ BC + B = B + C}
or
Q = AB + AC + A {∵B + B = 1}
or
Q = AB + A +AC {∵ AB + A = A + B}
or
Q = A + B + AC
or
Q = AC + A + B
or
Q = A + C + B {∵ AC + A = A + C}
or
Q = A + B + C