270L23-Sequential+Multiplication

270L23-Sequential+Multiplication - Multiplication...

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1 1 UM EECS 270 Fall 2009 Multiplication • Combinational – Parallel –Fast – High area cost • Sequential – Serial –S low ( n cycles for n -bit numbers) – Reasonable area cost 2 Multiplication Example 1011 Multiplicand Q (11 10 ) 1101 Multiplier M (13 10 ) X Partial Product P 0 (11 10 ) 0000 Partial Product P 1 (0 10 ) Partial Product P 2 (44 10 ) Partial Product P 3 (88 10 ) 10001111 Product P (143 10 )
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2 3 UM EECS 270 Fall 2009 Multiplication Example 1011 Multiplicand Q (11 10 ) 1101 Multiplier M (13 10 ) X Partial Product P 0 (11 10 ) 0000 Partial Product P 1 (0 10 ) Partial Product P 2 (44 10 ) Partial Product P 3 (88 10 ) 10001111 Product P (143 10 ) 00001011 Accumulated Sum (11 10 ) 00110111 Accumulated Sum (55 10 ) 4 Combinational Array Multiplier AB P * Block symbol + (5-bit) + (6-bit) + (7-bit) 00 000 0 a0 a1 a2 a3 b0 b1 b2 b3 0 p7. .p0 pp1 pp2 pp3 pp4 Digital Design Copyright © 2006 Frank Vahid
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3 5 UM EECS 270 Fall 2009 Sequential Multiplier V0.1 FSM Controller SHL SHR ADD LOAD m 0 2 n -bit LSH Register Q C 2 n -bit Register P 2 n -bit Adder n -bit RSH Reg M 6 Multiplier V0.1 Execution Trace PQ M C 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 Init 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 P Å P + Q 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 Q <<1, M >>1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 Q <<1, M >>1 0 0 1 1 0 1 1 1 0 0 1 0
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This note was uploaded on 04/18/2011 for the course EECS 270 taught by Professor David during the Spring '11 term at Michigan State University.

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270L23-Sequential+Multiplication - Multiplication...

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