Adders

Basic Adders+

What is Adder?

Adder :

In electronics an adder is digital circuit that perform addition of numbers.

In modern computer adder reside in the arithmetic logic unit (ALU).

Adders :

Adders are important not only in the computer but also in many types of digital systems in which the numeric data are processed.

Types of adder:

1. Half adder

2. Full adder

Half adder :

The half adder accepts two binary digits on its inputs and produce two binary digits outputs, a sum bit and a carry bit.

Carrycoutinput

input Sum

Full adder :

The full adder accepts two inputs bits and an input carry and generates a sum output and an output carry.

input

input

A Sum

Carry

B

Cout Cin

input

Half adder to Full adder

input

input

A

B

A

B

Sum

Cout

Half adder Half adder

Cin

Truth Table of Adder

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth Table of AdderA B Cin Cout ∑

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

A

B

Circuit of Adder

A

BX

Circuit of Adder

A

B

Cin

∑

Circuit of Adder

A

B

Cin

∑

Y

Circuit of Adder

A

B

Cin

∑

= A.B

Y

Circuit of Adder

A

B

Cin

∑

Cout

Cout= (A B). Cin + A.B

Circuit of Adder

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

0 0 0

Cout ∑

0 0

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

0 0 1

Cout ∑

0 1

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

0 1 0

Cout ∑

0 1

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

0 1 1

Cout ∑

1 0

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

1 0 0

Cout ∑

0 1

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

1 0 1

Cout ∑

1 0

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

1 1 0

Cout ∑

1 0

A

B

Cin

∑

Cout

Verification of Truth TableA B Cin

1 1 1

Cout ∑

1 1

Applications of Adder

THE BCD ADDER

BCD Adder

• Binary Coded Decimal Adder

• Just adds decimal digits

Binary Coded Decimal

• It is possible to represent decimal numbers simply by encoding each decimal digit in binary form called binary coded decimal

• Because there are 10 digits to represent, it is necessary to use four bits per digit.

From 0=0000 to 9=1001 by using 8421 code. For example: Convert 98 into BCD. 9 8 1001 1000 BCD representation was used in some early computers and many

handheld calculators.

Decimal DigitsDecimal Number BCD Equivalent

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

The BCD Adder

• BCD is a numerical code and can be used in arithmetic operations.• Addition is the most important operation in BCD.• Following are the steps to perform addition:

Step1Add the two BCD numbers, using the rules for binary

addition.

Step2If a 4-bit sum is equal to or less than 9, it is a valid BCD

number.

THE BCD ADDER

• Add the following BCD number

0011 + 0100

0011 3

+ 0100 + 4

0111 7

4-Bit Adder• A single full –adder is capable of adding two 1-bit numbers and

input carry.

• What happens if we want to add binary numbers with more than 1-bit?

• The concept of additional full-adders must be used i.e. to add 2-bit numbers two adders must be needed and to add 4-bit numbers four adders must be needed.

4-Bit Adder

Thanks!