carry look ahead adder

It is the adder used to eliminate the wastage of time occur at each stage of parallel binary adder.In this , by using only carry input signal , we can calculate the the carry output without going to calculate carry at each stage.it is commonly used only for 4 bit addition because further calculation will be more complex.

1. Page 1
carry Look-
ahead adder
By
Name :-Ashish Mani
College:- University college of engineering and
technology hazaribagh (Jharkhand)

2. Page 2
CONTENTS:-
 Introduction
Full adder ckt to show carry generation and propagation.
Truth table of full adder to show carry generation and carry
propagation.
 Expression for carry generation and propagation .
 Boolean expression of of carry out
 Carry look ahead structure
Four bit carry look ahead adder circuit.

3. Page 3
A look ahead carry adder is fast adder which improves speed
by reducing the amount of time required to determine carry
bits. It reduces the time which are delayed at each stage.
INTrodUcTIoN:-

4. Page 4
FULL ADDER CKT TO SHOW
CARRY
GENERATION AND
PROPAGATION

5. Page 5
TRUTH TAbLE OF FULL
ADDER TO SHOW CARRY
GENERATION AND
PROPAGATION INPUT OUTPUT
Row A B C
in
Sum C
out
0 0 0 0 0 0 No carry
generatio
n
C
out
=0
1 0 0 1 1 0
2 0 1 0 1 0 Carry
propagati
on
C
out
= C
in
3 0 1 1 0 1
4 1 0 0 1 0
5 1 0 1 0 1
6 1 1 0 0 1 Carry
generatio
n
C
out
= 1
7 1 1 1 1 1

6. Page 6
EXPRESSION FOR CARRY GENERATION AND
PROPAGATION
From truth table , carry generation in row 6
th
and 7
th

is given by :-

G
i = A
iB
i
 Similarly the carry propagation Pi occur with either Ai= 1 and Bi= 0 or
vice versa
P
i = A
i B
⊕
i
Gi is known as the carry Generate signal
Pi is known as the carry propagate signal
 The new expressions for the output sum and the carryout are given by:-
S
i
= P
i
C
⊕
i-1
C
i+1
= G
i
+ P
i
C
i

7. Page 7
Boolean expression of the carry outputs of various
stages
C
1
= G
0
+ P
0
C
0
C
2
= G
1
+ P
1
C
1
= G
1
+ P
1
(G
0
+ P
0
C
0
) = G
1
+ P
1
G
0
+ P
1
P
0
C
0

C
3
= G
2
+ P
2
C
2
= G
2
+ P
2
G
1
+ P
2
P
1
G
0
+ P
2
P
1
P
0
C
0

C
4
= G
3
+ P
3
C
3
= G
3
+ P
3
G
2
+ P
3
P
2
G
1
+ P
3
P
2
P
1
G
0
+ P
3
P
2
P
1
P
0
C
0

The general expression is :------
C
i+1
= G
i
+ P
i
G
i-1
+ P
i
P
i-1
G
i-2
+ ……. P
i
P
i-1
….P
2
P
1
G
0
+ P
i
P
i-1
….P
1
P
0
C
0
.

8. Page 8
Carry look-ahead adder’s structure can be divided into three parts:--
the carry propagate/generate generator
 the sum generator
 the look ahead carry generator
Fig. 3 Look-
Ahead Carry
generator

9. Page 9
Fig 1 + fig 2 + fig 3
4-bit Carry look ahead adder

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