EEL6323-S10-HLec019-Datapaths-4spp

# EEL6323-S10-HLec019-Datapaths-4spp - Lecture 19 Datapaths...

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1 Lecture 19: Datapaths Multipliers Shifters Comparators Counters LFSRs Multiplication Example: M x N-bit multiplication – Produce N M-bit partial products – Sum these to produce M+N-bit product 1100 : 12 10 0101 : 5 10 1100 0000 1100 0000 00111100 : 60 10 multiplier multiplicand partial products product 12 10 =0x2 0 + 0x2 1 + 1x2 2 + 1x2 3 5 10 =1x2 0 + 0x2 1 + 1x2 2 + 0x2 3 General Form Multiplicand: Y = (y M-1 , y M-2 , …, y 1 , y 0 ) Multiplier: X = (x N-1 , x N-2 , …, x 1 , x 0 ) Product: 111 1 00 0 0 22 2 MNN M j ii j ji i j jii j Py x x y         x 0 y 5 x 0 y 4 x 0 y 3 x 0 y 2 x 0 y 1 x 0 y 0 y 5 y 4 y 3 y 2 y 1 y 0 x 5 x 4 x 3 x 2 x 1 x 0 x 1 y 5 x 1 y 4 x 1 y 3 x 1 y 2 x 1 y 1 x 1 y 0 x 2 y 5 x 2 y 4 x 2 y 3 x 2 y 2 x 2 y 1 x 2 y 0 x 3 y 5 x 3 y 4 x 3 y 3 x 3 y 2 x 3 y 1 x 3 y 0 x 4 y 5 x 4 y 4 x 4 y 3 x 4 y 2 x 4 y 1 x 4 y 0 x 5 y 5 x 5 y 4 x 5 y 3 x 5 y 2 x 5 y 1 x 5 y 0 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 multiplier multiplicand partial products product Dot Diagram Each dot represents a bit partial products multiplier x x 0 x 15

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