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Adders. Binary Adders. Arithmetic circuit Addition Subtraction Division Multiplication. 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10. One bit in sum. Two bit in sum. Half Adder. A combinational circuit that performs the addition of two bits. Two inputs and two outputs.

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Binary adders
Binary Adders

  • Arithmetic circuit

    • Addition

    • Subtraction

    • Division

    • Multiplication


One bit in sum

Two bit in sum


Half adder
Half Adder

  • A combinational circuit that performs the addition of two bits.

  • Two inputs and two outputs.

  • Augend and Addend

  • Sum and Carry




Full adder
Full Adder

  • A combinational circuit that performs the addition of three input bits.

  • Three inputs and two outputs.

  • Sum and Carry




Binary ripple carry adder
Binary Ripple Carry Adder

  • Adders connected in cascade.

  • Carry output from one full adder connected to carry input of next full adder.





Why a carry lookahead adder
Why a Carry Lookahead Adder?

  • Practical design with reduced delay.

  • For a n- bit ripple carry adder

    • The longest delay path is 2n + 2.

    • 16 – bit ripple carry adder - delay is 34 gate delays


Carry lookahead adder
Carry Lookahead Adder

  • Designed by a transformation of the ripple carry adder design in which the carry logic over fixed groups of bits of the adder is reduced to two-level logic.


Design
Design

  • OR gate and one of the AND gates are removed to form each of the full adders to form the ripple carry adder.

  • Separate the parts of full adders not involving the carry propagation path from those containing the path.

  • First part of each full adder

    • partial full adder - PFA


  • Two outputs

    • Pi and Gi

    • From each PFA to ripple carry path

  • One input

    • Ci

    • From the carry path to each PFA


  • Pi = Ai XOR Bi - Propagate function

  • Gi = Ai . Bi - Generate function


  • WheneverPi = 1

    • Incoming carry is propagated through bit position from Ci+1.

  • WheneverPi = 0

    • carry propagation through bit position is blocked.


  • WheneverGi = 1

    • Carry output from the position is 1.

    • Regardless of value of Pi.

    • A Carry has been generated.

  • WheneverGi = 0

    • carry is not generated.

    • Ci+1 is 0.

    • Ci is also 0.


  • Generate and propagate functions correspond exactly to the half adder.

  • Essential in controling the values in ripple carry path.

  • PFA generates sum function by XOR of incoming carry, Ciand propagate function, Pi.


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