1. Multiplier D&C Example
Shantanu Dutt, UIC
= 185
X = 39
= = 7215
D&C breakup: ( ) X ( ) = (24(1011) ) X (24(0010) )
= 28(1011 X 0010) + 24(1011 x X 0010) X 0111
= 28( ) + 24( )
= bbbbbbbb = PL
+ bbbb bbbb = PM1
+ bbbb bbbb = PM2
bbbbbbbb = PH
_____________________
H/W Design 2 + PL +
PM1
Cost = 5 (n/2)-bit
Adders = 2.5 n FAs for RCAs
cin +
Cost = 3 2n-bit
adders = 6n FAs for RCAs
PM2
H/W Design 1
(n/2)-bit adders
cin
PL(n2n) +
PM1(n2n)
PM2(n2n) +
PH(n2n) +
cin
2n-bit adders + PH
Critical path:
Delay =
4*((n/2)-bit
adder delay) = 2n*(FA delay) for RCAs +
Critical path:
Delay =
2*((2n)-bit
adder delay) = 4n*(FA delay) for RCAs
n/2
n/2
n/2
n/2 2n