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10111001 = 185 X 00100111 = 39 = 0001110000101111 = 7215

+. +. P M2 (n 2n). P L (n 2n). P H (n 2n). P M1 (n 2n). Multiplier D&C Example. Shantanu Dutt, UIC. 10111001 = 185 X 00100111 = 39 = 0001110000101111 = 7215 D&C breakup: (10111001) X (00100111) = (2 4 (1011) + 1001) X (2 4 (0010) + 0111)

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10111001 = 185 X 00100111 = 39 = 0001110000101111 = 7215

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  1. + + PM2(n2n) PL(n2n) PH(n2n) PM1(n2n) Multiplier D&C Example Shantanu Dutt, UIC 10111001 = 185 X 00100111 = 39 = 0001110000101111 = 7215 D&C breakup: (10111001) X (00100111) = (24(1011) + 1001) X (24(0010) + 0111) = 28(1011 X 0010) + 24(1011 x 0111 + 1001 X 0010) + 1001 X 0111 = 28(00010110) + 24(01001101 + 00010010) + 00111111 = bbbbbbbb00111111 = PL + bbbb01001101bbbb = PM1 + bbbb00010010bbbb = PM2 + 00010110bbbbbbbb = PH _____________________ 0001110000101111 H/W Design 2 + PL + PM1 Cost = 5 (n/2)-bit Adders = 2.5 n FAs for RCAs cin + PM2 Cost = 3 2n-bit adders = 6n FAs for RCAs H/W Design 1 (n/2)-bit adders cin + 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

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