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CARRY PROPAGATE ADDER. AMIT HINGHER Computational Engineering. Basic Principle of a CPA. Adds two n-bit operands A = (a n-1 ..a 0 ), B=(b n-1 ..b 0 ) and an optional carry-in c in by performing carry propagation

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Carry propagate adder l.jpg

CARRY PROPAGATE ADDER

AMIT HINGHER

Computational Engineering


Basic principle of a cpa l.jpg
Basic Principle of a CPA..

  • Adds two n-bit operands A = (an-1..a0), B=(bn-1..b0) and an optional carry-in cin by performing carry propagation

  • Can be implemented as a combinational circuit using n full adders called the Ripple Carry Adder


Architecture l.jpg
ARCHITECTURE

a) Linear Structureb)Tree Structure


Arithmetic equation l.jpg
ARITHMETIC EQUATION

  • 2n cout + S = A + B + cin

  • 2n cout + Σn-1i=02i si

    = Σn-1i=0 2iai+ Σn-1i=0 2ibi+ cin

    = Σn-1i=0 2i (ai + bi) + cin

  • 2ci+1 + si = ai + bi+ ci ; I = 0,1..n-1

    where c0 = cin and cout = cn


Logical equation l.jpg
LOGICAL EQUATION

  • gi=ai bi

  • pi=ai  bi

  • si=pi  ci

  • Ci+1=gi + pi ci ; I = 0,1…n-1

    where c0 = cin & cout =cn


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Complexity Of CPA !!!

  • Computation time grows linearly with the operand word length n

  • Speeding up operation of CPA would require replacement by some faster adder structure

  • *(a) Symbol (b) Ripple Carry implementation of a CPA


Cpa carry propagate adder vs csa carry save adder l.jpg
CPA(Carry propagate Adder) VsCSA(Carry Save Adder)

* A four operand adder circuit


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Comparison (CPA vs CSA)

  • The two resulting adder arrays are similar in hardware requirements, logic structure and critical path lengths

  • Bit arrival time in the CPA is unequal (higher bit arrives later than the lower bits)

  • Comparatively slow


Why carry propagate adder l.jpg
Why Carry Propagate Adder ?

  • Performs carry propagation from each bit to higher bit positions

  • Addition results have to be converted to irredundant integer representation

  • Does not occupy a significant area of the chip

  • Less Power Consumption


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