JEE Main 2020 · 2 September · evening · Single correct · +4 / −1
In the following digital circuit, what will be the output at ‘Z’, when the
input (A, B) are (1, 0), (0, 0), (1, 1,), (0, 1)
- (a) 1, 1, 0, 1
- (b) 0, 1, 0, 0
- (c) 1, 0, 1, 1
- (d) 0, 0, 1, 0
Answer and solution
Answer (d) 0, 0, 1, 0
Solution
Physics sir · 2 steps
Name each gate's output, simplify with Boolean algebra, and the whole circuit becomes one gate.
- Label the gates. The top gate is a NAND, so X = A̅B̅. The bottom gate is an OR, so Y = A + B. The middle AND gives W = X · Y, and the final NOR takes X and W.
Z = X + XY̅ = X (1 + Y)̅ = X̅ = A̅B̅̅ = AB
(A, B) X = A̅B̅ Y = A + B W = XY Z = X + W̅ (1, 0) 1 1 1 0 (0, 0) 1 0 0 0 (1, 1) 0 1 0 1 (0, 1) 1 1 1 0 - So. The circuit behaves as a single AND gate, so Z is 1 only for (1, 1). The outputs are 0, 0, 1, 0, which is option (d).
The idea to keep. For a circuit with many gates, write each gate's output as an expression and simplify. Here X + XY = X (absorption), so the whole circuit reduces to one gate.
Answer from the NTA final answer key. Solution by PrepWiser.