Basic Combinational Circuit in Digital Logic
A Half Adder is a basic combinational circuit in digital logic that adds two single-bit binary numbers.
📥 Inputs: Two bits → A and B
📤 Outputs: Two results →
It is called a "half" adder because it cannot handle carry input from a previous stage (unlike the Full Adder).
In binary:
0 + 0 = 0 (Sum = 0, Carry = 0)
0 + 1 = 1 (Sum = 1, Carry = 0)
1 + 0 = 1 (Sum = 1, Carry = 0)
1 + 1 = 10 (Sum = 0, Carry = 1 → 1 is carry, 0 is sum)
| 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 the truth table:
As can be seen, the block diagram has two inputs and two outputs. The half adder's input states are represented by the augent and addent bits, while its output states are carry and sum.
The two logic gates listed below are used in the design of the half adder:
The Half Adder is designed by combining the 'XOR' and 'AND' gates and provide the sum and carry.
Imagine adding binary numbers 1 and 1:
📥 Inputs: A=1, B=1
📤 Half Adder output: Sum=0, Carry=1 → meaning "2" in binary (10).
This is exactly what happens inside the ALU (Arithmetic Logic Unit) of a CPU when it performs addition. The Half Adder is the building block for larger adders like the Full Adder, Ripple Carry Adder, and eventually the processor's arithmetic unit.
Half adders are fundamental components in various digital systems and arithmetic circuits. Here are some key applications:
Half adders are used to perform basic binary addition of single-bit numbers.
Multiple half adders can be combined to create full adders, which can add multi-bit binary numbers.
ALUs in processors use half adders and full adders to perform arithmetic operations.
Half adders are used in the design of digital counters and registers.
✅ Half Adder = simple circuit that adds two bits.
✅ Outputs: Sum (XOR), Carry (AND).
✅ Limitation: cannot add carry from a previous stage (that's why it's called "half").
✅ A fundamental building component for adding two numbers as inputs and producing two outputs is the half adder. The OR operation of two single-bit binary values is carried out by the adder. The half adder has two output states, "carry" and "sum," and two input states, the augent and addent bits.
Half adders are essential building blocks in digital logic circuits, forming the foundation for more complex arithmetic operations in computer systems.