The document discusses a carry look-ahead adder, emphasizing its efficiency in determining carry bits to enhance speed in addition operations. It includes details on full adder circuits, truth tables for carry generation, and boolean expressions for output carries. Additionally, it outlines the structure of the carry look-ahead adder, dividing its function into carry generation, propagation, and sum generation.

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

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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.

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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:-

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FULL ADDER CKT TO SHOW
CARRY
GENERATION AND
PROPAGATION

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TRUTH TAbLE OF FULL
ADDER TO SHOW CARRY
GENERATION AND
PROPAGATIONINPUT OUTPUT
Row A B Cin Sum Cout
0 0 0 0 0 0 No carry
generatio
n
Cout =0
1 0 0 1 1 0
2 0 1 0 1 0 Carry
propagati
on
Cout = Cin
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
Cout = 1
7 1 1 1 1 1

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EXPRESSION FOR CARRY GENERATION AND
PROPAGATION
 From truth table , carry generation in row 6th
and 7th
is given by :-
Gi = AiBi
 Similarly the carry propagation Pi occur with either Ai= 1 and Bi= 0 or
vice versa
Pi = Ai 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:-
Si= Pi C⊕ i-1
Ci+1= Gi + PiCi

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Boolean expression of the carry outputs of various
stages
C1 = G0 + P0C0
C2 = G1 + P1C1 = G1 + P1 (G0 + P0C0) = G1 + P1G0 + P1P0C0
C3 = G2 + P2C2 = G2 + P2G1 + P2P1G0 + P2P1P0C0
C4 = G3 + P3C3 = G3 + P3G2 + P3P2G1 + P3P2P1G0 + P3P2P1P0C0
The general expression is :------
Ci+1= Gi + PiGi-1 + PiPi-1Gi-2 + ……. PiPi-1….P2P1G0 + PiPi-1 ….P1P0C0.

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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

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

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