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## PowerPoint Slideshow about 'carry propagate adder' - arleen

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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

a) Linear Structureb)Tree Structure

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

- gi=ai bi
- pi=ai bi
- si=pi ci
- Ci+1=gi + pi ci ; I = 0,1…n-1
where c0 = cin & cout =cn

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) VsCSA(Carry Save Adder)

* A four operand adder circuit

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 ?

- 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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