Question

For the logic circuit given below, for
a) input \(A=0\) and input \(B=1\), and
b) input \(A=1\) and input \(B=1\), the output \(E\) is respectively

• A. zero and one.
• B. one and zero.
• C. zero and zero.
• D. one and one.

Hint:

Write the output of each AND gate in terms of A and B, then combine them with the OR gate.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
From the figure, the upper AND gate has inputs A and B, so \(C=A\cdot B\). The lower AND gate has inputs \(\bar{A}\) (through the NOT gate) and B, so \(D=\bar{A}\cdot B\).

Step 2: Output expression
The OR gate gives \(E=C+D=A\cdot B+\bar{A}\cdot B=B\left(A+\bar{A}\right)=B\).

Step 3: Case (a)
For \(A=0,\;B=1\): \(E=B=1\).

Step 4: Case (b)
For \(A=1,\;B=1\): \(E=B=1\). So the outputs are one and one, option (D).

Final Answer:
The output is one in both cases. \[ \boxed{\text{(D) }\text{one and one}} \]