Introduction to Half and Full Adder Circuit - Part 01 | Digital Logic Design |

Adder Circuit:
An adder is a digital logic circuit in electronics that implements addition of numbers.
Application of Adder Circuit:
In many computers and other kinds of processors adders are used in the arithmetic logic units or
ALU. They are also utilized in other parts of the processor, where they are used to
calculate addresses, table indices, increment and decrement operators, and similar operations.
Classification of adders:
Adders are classified into two types:
 Half adder
 Full adder
Half Adder and Full Adder
2
Saturday, November 24, 2018

 Half adder:
Truth Table:
3
Inputs Outputs
Augend (A) Addend (B) Carry Sum
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0
1+1=2 in decimal
is equal to 10 in
binary!
Truth table
output of AND
gate.
Truth table
output of XOR
gate.

Logic Diagram:
4
C=A.B
S=𝑨 ⊕ 𝑩 S= 𝑨𝑩 + 𝑨 𝑩=

Classification of adders:
 Full adder:
5

Truth Table:
6
Inputs Outputs
A B Carry in ‘C’ Sum ‘S’ Carry out
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
1+1+1=3 in decimal is
equal to 11 in binary!

Boolean Expression Using K Map:
For “SUM”
𝑆 𝐴, 𝐵, 𝐶 = Ʃ𝑚(1,2,4,7)
7
𝑩𝑪
00
𝑩𝑪
01
BC
11
𝑩 𝑪
10
𝐴
0
A
1
XOR Gate XNOR Gate
𝑆 = 𝐴𝐵𝐶 + 𝐴𝐵𝐶 + 𝐴𝐵𝐶 + 𝐴𝐵 𝐶
𝑆 = 𝐵 𝐴 𝐶 + 𝐴𝐶 + 𝐵 𝐴𝐶 + 𝐴𝐶
𝑺 = 𝑩 ⊕ (𝑨 ⊕ 𝑪)

Boolean Expression Using K Map:
For “CARRY OUT”
𝐶𝑜𝑢𝑡 𝐴, 𝐵, 𝐶 = Ʃ𝑚(3,5,6,7)
8
𝑩𝑪
00
𝑩𝑪
01
BC
11
𝑩 𝑪
10
𝐴
0
A
1
𝑪 𝒐𝒖𝒕 = 𝑨𝑪 + 𝑨𝑩 + 𝑩𝑪

Logic Diagram:
9

Introduction to Half and Full Adder Circuit - Part 01 | Digital Logic Design |

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