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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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Presentation Transcript
binary adders
Binary Adders
  • Arithmetic circuit
    • Addition
    • Subtraction
    • Division
    • Multiplication
slide3

0 + 0 = 0

  • 0 + 1 = 1
  • 1 + 0 = 1
  • 1 + 1 = 10

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.
slide12

Input carry 0110

  • A 1011
  • B 0011
  • Sum 1110
  • Output carry 0011
slide13

Input carry in the least significant position is 0.

  • Simple in concept.
  • Long circuit delay.
    • Many gates in the carry path.
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
slide17

Two outputs

    • Pi and Gi
    • From each PFA to ripple carry path
  • One input
    • Ci
    • From the carry path to each PFA
slide18

Pi = Ai XOR Bi - Propagate function

  • Gi = Ai . Bi - Generate function
slide19

WheneverPi = 1

    • Incoming carry is propagated through bit position from Ci+1.
  • WheneverPi = 0
    • carry propagation through bit position is blocked.
slide20

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.
slide21

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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