Half-Adder Circuit: Adding Two Binary Digits
Understand the fundamental building block of binary addition: the half-adder circuit. This guide explains its functionality, logic, and truth table, providing a clear understanding of how it adds two bits and produces a sum and carry output.
Half-Adder Circuit
Understanding the Half-Adder
A half-adder is a simple digital circuit that adds two binary digits (bits). It takes two inputs (let's call them 'x' and 'y') and produces two outputs: the sum (S) and the carry (C).
Think of it like adding single-digit numbers. If you add 1 + 0, the sum is 1 and there's no carry. If you add 1 + 1, the sum is 0 (because it's binary), and there's a carry of 1.
Truth Table for a Half-Adder
This table shows all possible input combinations and their corresponding outputs:
| x | y | S (Sum) | C (Carry) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Notice that the carry (C) is only 1 when both inputs (x and y) are 1. The sum (S) represents the least significant bit of the result.
Simplified Sum of Products (SOP) Expressions
These equations describe the half-adder's logic:
- S = x'y + xy' (Sum)
- C = xy (Carry)
(x' represents the NOT of x)
These equations can be used to build the logic diagram.
(A logic diagram would be included here in a complete document)