Question

A half-adder has

• A. One input only
• B. Two outputs only
• C. Two inputs and two outputs
• D. Three outputs

Hint:

- Half-Adder: Processes exactly 2 inputs and produces 2 outputs. It cannot handle an incoming carry bit from a previous stage. - Full-Adder: Processes exactly 3 inputs (including a carry-in bit) and produces 2 outputs.

Answer 1

The Correct Option is C

Concept: A half-adder is a basic combinational logic circuit used in digital electronics to execute the addition of two single-bit binary values. Let the two independent single-bit inputs be defined as \(A\) and \(B\). When performing binary addition, the sum can yield numbers requiring up to two distinct binary places. Therefore, the circuit must provide two separate outputs:
• Sum (\(S\)): Represents the least significant bit (LSB) resulting from the arithmetic addition.
• Carry (\(C\)): Represents the most significant bit (MSB) generated when both input bits are high. To understand this design thoroughly, let's examine the definitive truth table for a standard half-adder circuit: {|cc|cc|} Input A & Input B & Sum (S) & Carry (C)
0 & 0 & 0 & 0
0 & 1 & 1 & 0
1 & 0 & 1 & 0
1 & 1 & 0 & 1
From this truth table, we can derive the boolean logical expressions for each output:
• The Sum (\(S\)) output column is true when only one of the inputs is active. This corresponds directly to an Exclusive-OR logic gate expression: \[ S = A \oplus B = A\bar{B} + \bar{A}B \]
• The Carry (\(C\)) output column becomes true exclusively when both \(A\) and \(B\) are simultaneously high. This corresponds to a standard logical AND gate expression: \[ C = A \cdot B \] This complete structural breakdown clearly confirms that a half-adder requires exactly two inputs (\(A, B\)) and delivers exactly two outputs (\(Sum, Carry\)).