L2_Multiplication

# L2_Multiplication - YORK UNIVERSITY CSE4210 Multiplication CSE4210 Winter 2012 Mokhtar Aboelaze YORK UNIVERSITY Multiplication The simplest way of

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1 YORK UNIVERSITY CSE4210 Multiplication Mokhtar Aboelaze CSE4210 Winter 2012 YORK UNIVERSITY Multiplication • The simplest way of doing multiplication is repeated add and shift. • Easy to understand, simple hardware, but not very fast

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2 YORK UNIVERSITY AX MR AC MR 0 AX Current partial product C in C out n-bit adder S=s n-1 …s 1 s 0 Multiplicand A Multiplier B ] 1 1 [ 0 0 0 0 ) ( ) ( 0 if 0 1 if " + = = = n out out C MR C MR MR MR MR S MR AC AX AC S AX AX YORK UNIVERSITY Multiplication 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 a x x 0 a x 1 a x 2 a x 3 a
3 YORK UNIVERSITY Multiplication • Right shift • Left shift ( ) p p and 0 with 2 2 (k) ) 0 ( 1 ) ( ) 1 ( = = + = + p a x p p k j j j p p and 0 with a x 2 (k) ) 0 ( 1 - j - k ) ( ) 1 ( = = + = + p p p j j Multiplication by 2k aligns the number to the high order bits YORK UNIVERSITY a1 0 1 0 x1 0 1 1 =============== p (0) 0 0 0 0 +x 0 0 1 0 ---------------------- 2p (1) 01 0 1 0 p (1) 0 1 0 1 0 +x 1 0 1 0 --------------------------- 2p (2) 0 1 1 1 1 0 P (2) 0 1 1 1 1 0 +x 2 a0 0 0 0 -------------------------------- 2p (3) 0 0 1 1 1 1 0 P (3) 0 0 1 1 1 1 0 +x 3 0 1 0 ------------------------------------- 2p (4) 0 1 1 0 1 1 1 0 P (4) 0 1 1 0 1 1 1 0 0 1 0 0 1 1 =============== p (0) 0 0 0 0 2p (0) 0 0 0 0 0 +x 3 0 1 0 ----------------------------------

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## This note was uploaded on 02/13/2012 for the course CSE 4111 taught by Professor Edmonds during the Winter '12 term at York University.

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L2_Multiplication - YORK UNIVERSITY CSE4210 Multiplication CSE4210 Winter 2012 Mokhtar Aboelaze YORK UNIVERSITY Multiplication The simplest way of

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