The document discusses different types of adders used in digital circuits, including half adders, full adders, and ripple carry adders. A half adder adds two single binary digits and produces a sum and carry output. A full adder adds three binary digits and produces a sum and carry by using a combination of half adders and logic gates. A ripple carry adder is constructed by cascading multiple full adder blocks in series, where the carry output of one stage is fed into the next as the carry input.

1. Ripple carry adder, full
adder implementation
using half adder.
By
Md. Fazle Rabbi
16CSE057

2. 4.2
 An adder is a digital circuit that performs
addition of numbers.
 It can be constructed for many numerical
representations, such as binary-coded decimal
 The most common adders operate on binary
numbers.
What is Adder

3. 4.3
Half Adder
Full Adder
Types Of Adder

4. 4.4
The half adder adds two single binary
digits A and B.
It has two outputs, sum (S) and carry (C).
Sum = AB’+A’B. (XOR Gate)
Carry=A*B. (AND Gate)
Half Adder

5. 4.5
Half adder truth table
S=A B (Exclusive OR)
C=A.B (AND)

6. 4.6
A combinational circuit that adds 3 input bits to
generate a Sum bit and a Carry bit
Where X,Y,Z(Cin) are inputs and C & S are outputs.
Sum = A ⊕ B ⊕ Cin
Carry = AB + Cin (A ⊕ B)
Full Adder

7. 4.7
Full adder truth table
S= A ⊕ B ⊕ Cin
C=AB + Cin (A ⊕ B)

8. 4.8
Full Adder using Half Adder

9. 4.9
Ripple Carry Adder

10. 4.10
The ripple carry adder is constructed by
cascading full adder blocks in series
The carryout of one stage is fed directly to
the carry-in of the next stage
Carry bit gets rippled into the next stage.
For an n-bit ripple adder,
we require n full adders
Ripple Carry Adder- Introduction

11. 4.11
Ripple Carry Adder-Logic Diagram

12. 4.12
Ripple Carry Adder-Circuit Diagram

13. 4.13
Ripple Carry Adder-Truth Table

14. 4.14
Ripple Carry Adder-Delay
 A full adder becomes active only when its
carry in is made available by its adjacent less
significant full adder.
 When carry in becomes available to the full
adder, it starts its operation.
 It produces the corresponding output sum bit
and carry bit.

15. 4.15
Thank you