Question

The logic circuit shown in the figure is

• A. half adder
• B. XOR
• C. equality detector
• D. full adder

Hint:

An XNOR gate is also called:
1. Coincidence detector
2. Equality detector
Its output is high only when the inputs are identical.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The goal of this question is to analyze the given digital logic schematic with inputs $A$ and $B$, and determine its function.

Step 2: Key Formula or Approach:
We will find the Boolean expression at each node of the circuit to derive the overall output equation $Y(A, B)$.

Step 3: Detailed Explanation:

• The circuit has two inputs, $A$ and $B$, and consists of:
- A top AND gate whose inputs are directly connected to $A$ and $B$. Its output is:
\[ Y_1 = A \cdot B \]
- A bottom AND gate whose inputs are passed through inverters. The inputs are $\bar{A}$ and $\bar{B}$. Its output is:
\[ Y_2 = \bar{A} \cdot \bar{B} \]
- A final OR gate that sums the outputs of the two AND gates:
\[ Y = Y_1 + Y_2 = AB + \bar{A}\bar{B} \]

• The expression $AB + \bar{A}\bar{B}$ is the Boolean expression for an XNOR gate (coincidence or equality gate).

• Let us look at the truth table of XNOR:
- For $A=0, B=0 \implies Y = 1$
- For $A=0, B=1 \implies Y = 0$
- For $A=1, B=0 \implies Y = 0$
- For $A=1, B=1 \implies Y = 1$

• The output is high ($1$) if and only if both inputs are equal ($A = B$). Therefore, this circuit serves as an equality detector.

Step 4: Final Answer:
The logic circuit is an equality detector, which corresponds to Option (C).