Table of Contents

### 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.

Categories: Computer Organization

### 0 Comments

This site uses Akismet to reduce spam. Learn how your comment data is processed.