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CARRY PROPAGATE ADDER

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

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  1. CARRY PROPAGATE ADDER AMIT HINGHER Computational Engineering

  2. 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

  3. ARCHITECTURE a) Linear Structureb)Tree Structure

  4. 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

  5. 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

  6. 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

  7. CPA(Carry propagate Adder) VsCSA(Carry Save Adder) * A four operand adder circuit

  8. 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

  9. 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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