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Table of contents
1.
Introduction
2.
What is a Combinational circuit?
3.
Half Adder
3.1.
Block Diagram
3.2.
Truth Table
3.3.
Circuit Diagram
4.
Full Adder
4.1.
Block diagram
4.2.
Truth Table
4.3.
Circuit Diagram
5.
N-Bit Parallel Adder
5.1.
4 Bit Parallel Adder
5.1.1.
Block Diagram
6.
FAQs
7.
Key Takeaways
Last Updated: Mar 27, 2024

Adder

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Introduction

A digital circuit that adds two numbers together is known as an adder. Adders are utilised in the arithmetic logic units of many computers and other types of processors (ALUs). They're also used to calculate addresses, table indices, increment and decrement operators, and other operations in other CPU(Central Processing Unit) areas.

Although adders can be built for various number representations, such as binary-coded decimal or excess-3, binary numbers are the most frequent. It is simple to convert an adder into an adder–subtractor when two's complement or ones' complement is used to represent negative values. 

 

What is a Combinational circuit?

A combinational circuit is one in which the various gates, such as the encoder, decoder, multiplexer, and Demultiplexer, are combined. The following are some of the properties of combinational circuits:

  • At any given point, the output of a combinational circuit is solely determined by the levels present at the input terminals.
  • There is no memory in the combinational circuit. The last state of the input does not affect the circuit's current state.
  • A combinational circuit has ‘n’ number of inputs and ‘m’ number of outputs.

Source: Combinational Circuit

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Half Adder

A half adder is a two-input, two-output combinational logic circuit. The half adder circuit adds two binary numbers, A and B; both are single bits. It's the fundamental building element for adding two single-bit numbers together. Carry, and Sum are the two outputs of this circuit.

Block Diagram

Source: Half Adder

Truth Table

 

Circuit Diagram

Source: Circuit

Full Adder

The Full Adder circuit was created to address the drawbacks of the Half Adder circuit. It can carry ‘C’ and add two one-bit values, A and B. The complete adder is a combinational circuit with three inputs and two outputs.

Block diagram

Source: Full Adder

Truth Table

Circuit Diagram

Source: Circuit

N-Bit Parallel Adder

Only two single-digit binary numbers and a Carry input can be added with the Full Adder. However, we must add binary integers that are much larger than one bit in practice. The n-bit parallel adder is used to add two n-bit binary values. It makes use of a cascade of complete adders. The previous full adder's Carry output is connected to the following full adder's Carry input.

4 Bit Parallel Adder

The LSB of the four-bit words A and B are represented by A0 and B0 in the block diagram. Hence The lowest stage is Full Adder-0. As a result, its Cin has been set to 0. The rest of the connections are identical to those depicted in the n-bit parallel adder in the following figure. A four-bit parallel adder is a common logic circuit.

Block Diagram

Source: Block Diagram

Must Read Shift Registers in Digital Electronics

FAQs

  1. What is an Adder in digital electronics?
    A digital circuit that adds two numbers together is known as an adder. Adders are utilised in the arithmetic logic units of many computers and other types of processors (ALUs).
     
  2. What are the values of Sum and Carry in half adder?
    For Sum,
    S = A'B+AB'
    For Carry,
    C = AB
     
  3. What are the values of Sum and Carry in full adder?
    For Sum,
    S= A’B’C+A’BC’+AB’C’+ABC
    For Carry,
    C= AB+AC+BC
     
  4. What if A=0, B=0, Cin=0 in the full adder? What will the Sum and Carry value be?
    If A=0, B=0, Cin=0 in the full adder, the Sum and Carry will be 0.
     
  5. Write real-time application of half adder.
    Half adders can be found in computers, calculators, and digital measuring instruments in real-time applications.

Key Takeaways

In this article, we have discussed the concept of adders. These are combinational circuits that are being used in digital electronics. We have seen half adder and full adder their truth table and their circuits. An adder is a digital circuit that adds two numbers together. Adders are utilised in the arithmetic logic units of many computers and other processors.

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