Semiconductors

JEE Main level, single correct, medium

130 of 209

Question 130 of 209

For the given logic circuit, which of the following inputs combination will make both LED−1-1 and LED−2-2 to glow?

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Answer: (C) A=1,B=0,C=1A = 1, B = 0, C = 1

Let the output of the OR gate be Y1Y_1.

Y1=A+BY_1 = A + B

For LED-1 to glow, Y1Y_1 must be 11, which means A+B=1A + B = 1.

Let the output of the first AND gate be Y2Y_2.

Y2=Y1⋅C=(A+B)⋅CY_2 = Y_1 \cdot C = (A + B) \cdot C

Let the output of the second AND gate be Y3Y_3.

Y3=A⋅Y2=A⋅(A+B)⋅CY_3 = A \cdot Y_2 = A \cdot (A + B) \cdot C

For LED-2 to glow, Y3Y_3 must be 11.

Simplifying the Boolean expression for Y3Y_3:

Y3=(A⋅A+A⋅B)⋅CY_3 = (A \cdot A + A \cdot B) \cdot C

Y3=(A+AB)⋅CY_3 = (A + AB) \cdot C

Y3=A(1+B)⋅CY_3 = A(1 + B) \cdot C

Y3=A⋅CY_3 = A \cdot C

For Y3=1Y_3 = 1, we require A=1A = 1 and C=1C = 1.

If A=1A = 1, then Y1=1+B=1Y_1 = 1 + B = 1 for any value of BB, satisfying the condition for LED-1 to glow.

From the given options, the combination A=1,B=0,C=1A = 1, B = 0, C = 1 satisfies these conditions.

Answer: A=1,B=0,C=1A = 1, B = 0, C = 1

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