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CARDAMOM PLANTERS ASSOCIATION COLLEGE�(RE-ACCREDITED WITH ‘B’ GRADE BY NAAC)�PANKAJAM NAGAR, BODINAYAKANUR – 625513��DEPARTMENT OF CS & IT��ARITHMETIC BUILDING BLOCKS

Prepared by

S. Rohini

Assistant professor

Department of CS & IT

CPA college

Bodinayakanur

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ADDER

An Adder is a device that can add two binary digits. It is a type of digital circuit that performs the operation of additions of two number.

It is mainly designed for the addition of binary number, but they can be used in various other applications like binary code decimal, address decoding, table index calculation, etc.

There are two types of Adder. One is Half Adder, and another one is known as Full Adder.

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HALF ADDER

There are two inputs and two outputs in a Half Adder.
Inputs are named as A and B, and the outputs are named as Sum (S) and Carry (C).
The Sum is X-OR of the input A and B. Carry is AND of the input A and B.
With the help of half adder, one can design a circuit that is capable of performing simple addition with the help of logic gates.

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Let us first take a look at the addition of single bits.

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

These are the least possible single bit combinations. But the result for 1 + 1 =10. This problem can be solved with the help of an EX-OR gate. The sum results can be re-written as a 2-bit output.

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Thus the above combination can be written as:

0 + 0 = 00

0 + 1 = 01

1 + 0 = 01

1 + 1 = 10

Here the output “1” of “10” becomes the carry-out. SUM is the normal output and the CARRY is the carry-out.

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Input A	Input B	Sum	Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Truth table and Circuit Diagram

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K-Map for Sum & Carry

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The main disadvantage of this circuit is that it can only add two inputs and if there is any carry, it is neglected. Thus, the process is incomplete.
To overcome this difficulty Full Adder is designed. While performing complex addition, there may be cases when you have to add two 8 bit bytes together. This can be done with the help of Full Adder.

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FULL ADDER

The full adder is a little more difficult to implement than a half adder.
The main difference between a half adder and a full adder is that the full-adder has three inputs and two outputs.
The two inputs are A and B, and the third input is a carry input C_IN. The output carry is designated as C_OUT, and the normal output is designated as S.

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Truth table and Circuit Diagram

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K-Map for Sum & Carry

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Logic gate diagram-Full Adder

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The output S is an EX-OR between the input A and the half-adder SUM output B. The C_OUT will be true only if any of the two inputs out of the three are HIGH or at logic 1.
Thus, a full adder circuit can be implemented with the help of two half adder circuits.
The first half adder circuit will be used to add A and B to produce a partial sum.
The second half adder logic can be used to add C_IN to the sum produced by the first half adder circuit. Finally, the output S is obtained