Question

In the logic circuit given, \(\mathrm{A}, \mathrm{B}\) and C are the inputs and Y is the output. The output Y is HIGH

• A. for all the HIGH inputs.
• B. for all the LOW inputs.
• C. when \(\mathrm{A}=1,\text{ }\mathrm{B}=0,\mathrm{C}=0\)
• D. when \(\mathrm{A}=1,\text{ }\mathrm{B}=0,\mathrm{C}=1\)

Hint:

Find the output of the NOR gate first, then feed it with input A into the AND gate.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
From the figure, B and C go into a NOR gate. Its output and the input A go into an AND gate to give Y.
So \(Y=A\cdot\overline{(B+C)}\).

Step 2: Condition for HIGH output
Y is HIGH only when \(A=1\) and \(\overline{B+C}=1\), that is \(B+C=0\), so \(B=0\) and \(C=0\).

Step 3: Compare the options
Option (C) gives \(A=1,B=0,C=0\) and \(Y=1\cdot\overline{0}=1\). Option (D) gives \(B+C=1\), so Y is 0.

Final Answer:
Y is high when A is 1 and both B and C are 0. \[ \boxed{\text{(C) }\text{when }A=1,\ B=0,\ C=0} \]