Question

Two binary signals ‘a’ and ‘b’ are to be compared. When two signals are equal, then output expression is _______.

• A. \( a \cdot \bar{b} + \bar{a} \cdot b \)
• B. \( ab + \bar{a}\bar{b} \)
• C. \( \bar{a}b \)
• D. \( ab \)

Hint:

Equality comparator = \( ab + \bar{a}\bar{b} \). True when both bits are same.

Answer 1

The Correct Option is B

Step 1: Equality Condition
The output should be high when \( a = b \) i.e., both are 0 or both are 1.
Step 2: Write Boolean Expression
- Case 1: \( a = 1, b = 1 \Rightarrow ab = 1 \)
- Case 2: \( a = 0, b = 0 \Rightarrow \bar{a} \bar{b} = 1 \)
Combine both using OR: \[ \text{Output} = ab + \bar{a}\bar{b} \] Step 3: Verify Other Options
- (1) = XOR logic → incorrect
- (3) = only 1 case (mismatch)
- (4) = just 1 case satisfied
Conclusion:
Option (2) is correct — it gives HIGH output only when inputs are equal.