09-05-2011, 03:07 PM
[attachment=13473]
CARRY PROPAGATE ADDER
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
ARITHMETIC EQUATION
2n cout + S = A + B + cin
2n cout + Σn-1i=0 2i 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 !!!
CPA(Carry propagate Adder) Vs CSA (Carry Save Adder)
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
CARRY PROPAGATE ADDER
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
ARITHMETIC EQUATION
2n cout + S = A + B + cin
2n cout + Σn-1i=0 2i 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 !!!
CPA(Carry propagate Adder) Vs CSA (Carry Save Adder)
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