Question

What is the half adder?

Answer 1

A half adder is a simple digital circuit that adds two single-bit binary numbers. It has two inputs and two outputs:

Inputs:

1. A: The first bit (input).
   

1. B: The second bit (input).
   

Outputs:

1. Sum (S): This is the result of adding the two bits (A and B).
   

1. Carry (C): This is the carry bit, which tells you if there’s an overflow when adding the two bits (like how 1 + 1 in decimal gives you a carry of 1).
   

Truth Table:

| A | B | Sum (S) | Carry (C) |
|---|---|---------|-----------|
| 0 | 0 |    0    |     0     |
| 0 | 1 |    1    |     0     |
| 1 | 0 |    1    |     0     |
| 1 | 1 |    0    |     1     |

Explanation:

1. When both inputs are 0 (A=0, B=0), the sum is 0, and there's no carry.
   

1. When A is 0 and B is 1 (or vice versa), the sum is 1, and there's no carry.
   

1. When both inputs are 1 (A=1, B=1), the sum is 0, but we get a carry of 1 (because 1 + 1 equals 2, which is written as 10 in binary, so 0 is the sum and 1 is the carry).
   

Logic Circuit:

1. The Sum (S) is produced using an XOR (exclusive OR) gate:  
   

  \( S = A \oplus B \)

1. The Carry (C) is produced using an AND gate:  
   

  \( C = A \land B \)

A half adder is a basic building block in digital electronics, and it's often used to build more complex adders like the full adder.