Consider the circuit shown below. In a certain steady state, the line Y is at '1'. What are the possible values of A, B and C in this state? [Circuit: Three inputs A, B, C feed into a gate network. A and B are inputs to a NAND gate whose output, together with C, feeds into another NAND gate producing Y.] A. A = 0, B = 0, C = 1 B. A = 0, B = 1, C = 1 C. A = 1, B = 0, C = 1 D. A = 1, B = 1, C = 1

GATE 1999 · Digital Logic · Circuit Output · medium

Answer: D. A = 1, B = 1, C = 1 — Only this combination makes NAND(A,B) = NAND(1,1) = 0, so Y = NAND(0, C) = NAND(0,1) = 1.

1. Analyze the circuit structure: For the two-NAND chain: G1_out = NAND(A,B), Y = NAND(G1_out, C). For Y=1 we need: NOT(G1_out=1 AND C=1), i.e., G1_out=0 OR C=0.
2. Evaluate each option: Option A: A=0,B=0,C=1 -> G1=NAND(0,0)=1, Y=NAND(1,1)=0. Y=0, not 1. Option B: A=0,B=1,C=1 -> G1=NAND(0,1)=1, Y=NAND(1,1)=0. Y=0, not 1. Option C: A=1,B=0,C=1 -> G1=NAND(1,0)=1, Y=NAND(1,1)=0. Y=0, not 1. Option D: A=1,B=1,C=1 -> G1=NAND(1,1)=0, Y=NAND(0,1)=1. Y=1. Correct!