Introduction
- Adder is a very good example of Combinational Logic Circuits.
Definition
- An adder is a fundamental component in digital electronics devices and is used to perform arithmetic operations, specifically addition.
Characteristics
- Adders are found in ALU of CPU.
- Adders do not have their memory.
- Their output depends solely on the current inputs.
Types of Adder
(I) Half Adder
- This adder adds two single-bit binary numbers only(say X and Y).
- This adder results in two output forms – Sum (S) and Carry-out (Co).
Truth Table:
| X | Y | Sum (S) | Carry-out (Co) |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Logic Equations:
- Sum (S) = X ⊕ Y (XOR gate)
- Carry-out (Co) = X ⋅ Y (AND gate)
Circuit Diagram:
(II) Full Adder
- This adder adds three single-bit binary numbers (A, B, and Carry-in [Ci]).
- This adder results two output forms – Sum (S) and Carry-out (Co).
Truth Table:
| A | B | Ci | Sum (S) | Carry-out (Co) |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
Logic Equations:
- Sum (S) = A ⊕ B ⊕ Ci
- Carry-out (Co) = (A ⋅ B) + (Ci ⋅ (A ⊕ B))
Circuit Diagram:
(III) Ripple Carry Adder
- This adder is an advance form of Full Adders.
- This adder adds multi-bit binary numbers by cascading full adders.
- It consists of N-full adders for N-bit numbers addition.
- It gives Sum bits and a final Carry-out.
- The Carry-out value from each full adder is connected to the Carry-in of the next higher-order full adder.
- Demerits:
- It shows propagation delay i.e., the time taken for the carry to propagate through all full adders, leading to slower addition as the number of bits increases.
(IV) Look-Ahead Carry Adders
- Look-ahead carry adders are advanced form of Ripple Carry Adders and other more complex adder architectures can be used to reduce propagation delay.
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