Semiconductors

JEE Main level, single correct, medium

129 of 209

Question 129 of 209

Refer to the logic circuit given below. For two inputs (A=1,B=1)(A=1, B=1) and (A=0,B=1)(A=0, B=1), output (Y)(Y) will be __________.

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Answer: (C) 0,00, 0 respectively

From the given logic circuit, we can determine the Boolean expression for the output YY.

The output of the NOT gate is Aˉ\bar{A}.

The inputs to the OR gate are Aˉ\bar{A} and BB, so its output is Aˉ+B\bar{A} + B.

The inputs to the AND gate are Aˉ\bar{A} and BB, so its output is Aˉ⋅B\bar{A} \cdot B.

These two outputs are fed into a NOR gate. The final output YY is given by:

Y=(Aˉ+B)+(Aˉ⋅B)‾Y = \overline{(\bar{A} + B) + (\bar{A} \cdot B)}

Simplifying the Boolean expression:

Y=Aˉ+B+AˉB‾Y = \overline{\bar{A} + B + \bar{A}B}

Y=Aˉ+B(1+Aˉ)‾Y = \overline{\bar{A} + B(1 + \bar{A})}

Y=Aˉ+B‾Y = \overline{\bar{A} + B}

Using De Morgan's laws:

Y=Aˉ‾⋅Bˉ=A⋅BˉY = \overline{\bar{A}} \cdot \bar{B} = A \cdot \bar{B}

Now, we evaluate YY for the given input combinations:

For A=1,B=1A = 1, B = 1:

Y=1⋅1ˉ=1⋅0=0Y = 1 \cdot \bar{1} = 1 \cdot 0 = 0

For A=0,B=1A = 0, B = 1:

Y=0⋅1ˉ=0⋅0=0Y = 0 \cdot \bar{1} = 0 \cdot 0 = 0

Therefore, the outputs are 00 and 00 respectively.

Answer: 0,00, 0 respectively

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