Question

A full adder and an XOR gate are used to design a digital circuit with inputs \( X, Y, Z \), and output \( F \), as shown below. The input \( Z \) is connected to the carry-in input of the full adder.
If the input \( Z \) is set to logic ‘1’, then the circuit functions as _________ with \( X \) and \( Y \) as inputs.

• A. an adder
• B. a subtractor
• C. a multiplier
• D. a binary to Gray code converter

Hint:

When a carry-in is set to ‘1’ in a full adder, it changes the adder’s operation to subtraction.

Answer 1

The Correct Option is B

A full adder is a digital circuit that adds two binary digits and a carry-in. However, in this circuit, \( Z \) is connected to the carry-in input and is set to logic ‘1’. This configuration will cause the circuit to subtract \( Y \) from \( X \). 
Here's why:
The XOR gate is used to perform a subtraction operation in digital circuits, where the input \( X \) and \( Y \) are processed with the logic ‘1’ carry-in (i.e., the full adder behaves like a subtractor with the carry-in being ‘1’).
In this case, \( X \) and \( Y \) will be subtracted, producing the desired difference. 
Thus, the overall circuit functions as a subtractor when \( Z \) is set to ‘1’. Hence, the correct answer is (B).