Unit 4 Carry Look Ahead Adder PDF

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 st...

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. Page 1  INTRODUCTION:- 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. Page 2 FULL ADDER CKT TO SHOW CARRY GENERATION AND PROPAGATION Page 3  truth table of full adder to show carry generation and propagation INPUT OUTPUT Row A B Cin Sum Cout 0 0 0 0 0 0 No carry 1 0 0 1 1 0 generatio n Cout =0 2 0 1 0 1 0 Carry 3 0 1 1 0 1 propagati on 4 1 0 0 1 0 Cout = Cin 5 1 0 1 0 1 6 1 1 0 0 1 Carry 7 1 1 1 1 1 generatio n Cout =41 Page  EXPRESSION FOR CARRY GENERATION AND PROPAGATION  From truth table , carry generation in row 6th and 7th is given by :- G i = A i Bi  Similarly the carry propagation Pi occur with either Ai= 1 and Bi= 0 or vice versa Pi = Ai ⊕Bi 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 ⊕ Ci-1 Ci+1= Gi + PiCi Page 5 Boolean expression of the carry outputs of various stages C1 = G0 + P0 C0 C2 = G1 + P1C1 = G1 + P1 (G0 + P0C0) = G1 + P1G0 + P1P0C0 C 3 = G 2 + P 2 C 2 = G 2 + P 2 G1 + P 2 P1 G0 + P 2 P1 P0 C 0 C 4 = G 3 + P 3 C 3 = G 3 + P 3 G2 + P 3 P2 G1 + P 3 P2 P1 G0 + P 3 P2 P1 P0 C 0 The general expression is :------ Ci+1= Gi + PiGi-1 + PiPi-1Gi-2 + ……. PiPi-1….P2P1G0 + PiPi-1 ….P1P0C0. Page 6 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 Page 7  Fig 1 + fig 2 + fig 3 4-bit Carry look ahead adder Page 8 Page 9