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CARRY LOOK AHEAD ADDER

IT IS TOTALLY ON CLA.

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CARRY LOOK AHEAD ADDER

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  1. CARRY LOOK AHEAD ADDER Poulomi Ghosh Academy Of Technology CSE, 6th Sem Roll-06

  2. WHAT IS CARRY LOOK AHEAD ADDER ??? • A carry-look ahead adder (CLA) • is a type of adder • used in digital logic to reduce carry • propagation time.

  3. Problem caused by ripple carry adder… Ripple Carry Adders take the time more to calculate the carry alongside the sum as well as to propagate the carry.

  4. Inventors of Carry Look Ahead Adder… • Charles Babbage first lighted on the problems caused by ripple carry adders. • Gerald Rosenberger of IBM first gave a patent of Carry Look Ahead Adders.

  5. Functions Of Carry Look Ahead Adder… • A carry-look ahead adder improves speed by reducing the amount of time required to determine carry bits. • The carry-look ahead adder calculates one or more carry bits before the sum, which reduces the wait time to calculate the result of the larger value bits.

  6. Carry look ahead depends on two things : • Calculating, for each digit position, whether that position is going to propagate a carry if one comes in from the right. • Combining these calculated values to be able to deduce quickly whether, for each group of digits, that group is going to propagate a carry that comes in from the right.

  7. The fact when carry will generate… • When both bits Ai and Bi are 1, or • When one of the two bits is 1 and the carry-in (carry of the previous stage) is 1.

  8. Circuit Diagram of a 4-bit Carry Look Ahead Adder… 4-Bit Carry Look Ahead Adder

  9. Propagate & generate… Propagate P and Generate G in a CLA is given by, Pi=Ai Bi Gi=Ai Bi Ai Pi Bi Gi

  10. Sum & carry generation… The new expressions for the output sum and the carryout is given by, Si = Pi Ci-1 Ci+1 = Gi +Pi Ci Pi Si Ci-1 Ci+1 Gi

  11. Carry outputs… The Boolean expressions for carry outputs of various stages can be written as follows : C1=G0+P0.C0 C2=G1+G0. P1+C0. P0. P1 C3=G2+G1. P2+G0. P1. P2+C0. P0. P1. P2 C4=G3+G2. P3+G1. P2. P3+G0. P1. P2. P3+C0. P0. P1. P2. P3

  12. Implementation of 4-bit carry look ahead adder… • The Carry Look Ahead 4-bit adder can also be used in a higher-level circuit by having each CLA Logic circuit produce a propagate and generate signal to a higher-level CLA Logic circuit. • The group propagate (PG) and group generate (GG) for a 4-bit CLA are : PG = P0 . P1 . P2 . P3 GG = G3 + G2 . P3 + G1 . P3 . P2 + G0 . P3 . P2 . P1

  13. Advantage of carry look ahead adder… • Like ripple carry adder we need not to wait for the propagation of carries to get the sum. • If we build the circuit totally out of 2-input AND gates or 2-input OR gates, then the best we can do is about O(log N) where N is the number of bits in the addition. Still, that's far more efficient than O(N).

  14. Disadvantage of carry look ahead adders… The disadvantage of CLA is that the carry logic block gets very complicated for more than4-bits. For that reason, CLAs are usually implemented as 4-bit modules and are used in a hierarchical structure to realize adders that have multiples of 4-bits.

  15. Bibliography… Books: • Salivahanan S., Arivazhagan S., Digital Electronics : Principles, Devices and Applications, Vikas Publishing House Pvt. Ltd. Internet: • en.wikipedia.org/wiki/Carry-lookahead_adder • users.encs.concordia.ca/~asim/coen312/Lectures/CLA_adder.pdf • faculty.kfupm.edu.sa/COE/abouh/Lesson3_3.pdf

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