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# CARRY PROPAGATE ADDER - PowerPoint PPT Presentation

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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#### Presentation Transcript

AMIT HINGHER

Computational Engineering

### 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

* 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