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GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 27

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What statement is correct for $f(A, B)$ in the following circuit?

  1. $f(A, B)=\overline{\overline{A \cdot B} \cdot(A+B)}$ when Control $=1$
  2. $f(A, B)=A \cdot B$ when Control $=0$
  3. $f(A, B)=\overline{A}+\overline{B}$ when Control $=1$
  4. $f(A, B)=\overline{A} \cdot \overline{B}$ when Control $=0$
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2 Answers

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NAND output is one if atleat one input is 0

OR output is 1 when atleast 1 input is 1

 

when control signal is 0

Top NAND will be 1 OR will be $OR(0,A,B)=OR(A,B)$ resulting in

$NAND(1,A+B)=\overline{A+B}=\overline{A}.\overline{B}$

 

when control input is 1 top NAND will give $\overline{A.B}$

OR will give 1 (or is 1 when atleast 1 is 1)

finally give $\overline{\overline{A.B}.1}=\overline{\overline{AB}}+0=AB$

 

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Correct Answer is D

In the above circuit 3 Input NAND and 3 input OR is present with A and B as input and common control input.

Case 1: Control Input is 1

NAND = (A.B.1)' = (A.B)'

OR = 1+A+B =1

=((A.B)'.1)' = A.B

 

Case 2: Control Input is 0

NAND = (A.B.0)' = 1

OR = 0+A+B = A+B

=(1.(A+B))' = A'.B'

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