The document explains the concepts of half adder and full adder in digital electronics. A half adder takes two binary inputs and produces a sum and carry output, while a full adder takes three inputs and also produces a sum and carry. Additionally, it details the formulas for calculating sum and carry in both types of adders.

1. Half Adder and Full Adder
Khan Mohammad Shayshab Azad
161002036

2. content
•Definition of adder .
•Types of Adder.
•Explain Half Adder and Full Adder.

3. Definition of adder
•An adder is a digital logic circuit in electronics that
implements addition of numbers. In many computers
and other types of processors, adders are used to
calculate addresses, similar operations and table indices
in the ALU and also in other parts of the processors.
These can be built for many numerical representations
like excess-3 or binary coded decimal.

4. 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.
INPUTS OUTPUTS
A B SUM CARRY
0 0 0 0
o 1 1 0
1 0 1 0
1 1 0 1
SUM =A’B+AB’
= A ⊕B
CARRY =AB

5. FULL ADDER
• The full adder accepts three binary digits on its inputs and produce two
binary digits outputs a sum bit and a carry bit.
INPUT OUTPUT
A B C SUM CARR
Y
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
SUM = A′B′C + A′BC′ + AB′C′ + ABC
= A′(B′C+BC′) + A (B′C′+BC)
= A′(B ⊕ C) + A(B ⊕ C)′
=A’P +AP’ let B ⊕ C=P
=A ⊕p
= A ⊕ B ⊕ C
CARRY=A’BC+AB’C+ABC’+ABC
=C(A’B+AB’)+AB(C’+C)
=C(A ⊕B)+AB

6. ThankYou !