October 5 Register to vote! Go to the State Fair! (15-24 October) Help with a user study! (Peter Parente parente@cs.unc.edu) How many struggling with Assignment 5,6,7? Questions? Chapter 4 – Multiplication/Division 10/5/2004 Comp 120 Fall 2004

Multiplication Facts N digit number TIMES a M digit number produces: ? 32 bit number TIMES a 32 bit number produces: ? an (N+M) digit number a 64 bit number 123 x 45 615 492 5535 101 x 11 1111 10/5/2004 Comp 120 Fall 2004

Multiplication: Implementation S t a r t D o n e 1 . T s t M u l i p r a A d m c h P g 2 S f b 3 M u l t i p l i e r = 1 M u l t i p l i e r = t N o : < 3 2 r e p e t i t i o n s 3 2 n d r e p e t i t i o n ? Y e s : 3 2 r e p e t i t i o n s 10/5/2004 Comp 120 Fall 2004

Second Version 10/5/2004 Comp 120 Fall 2004 S t a r t M u l t i p l i . T s t M u l i p r a A d m c h f P g 2 S b 3 3 2 b i t s M u l t i p l i e r = 1 M u l t i p l i e r = M u l t i p l i e r 3 2 - b i t A L U S h i f t r i g h t 3 2 b i t s S h i f t r i g h t P r o d u c t C o n t r o l t e s t W r i t e 6 4 b i t s i f t t h e M u l t i p l i e r r e g i s t e r r i g h t 1 b i t N o : < 3 2 r e p e t i t i o n s 3 2 n d r e p e t i t i o n ? Y e s : 3 2 r e p e t i t i o n s 10/5/2004 Comp 120 Fall 2004

Example for second version 0010 1100 0001 0110 0010 0001 0000 Test true shift right 4 0001 1000 0000 1100 0010 0001 Test false shift right 3 0011 0000 0001 1000 0101 0010 2 0010 0000 0001 0000 1011 0101 1 0000 0000 1011 Initial Product Multiplicand Multiplier Step Iteration 10/5/2004 Comp 120 Fall 2004

Final Version S t a r t D o n e 1 . T s t P r d u c a A m l i p h f g 2 S b 3 M u l t i p l i c a n d 3 2 b i t s P r o d u c t = 1 P r o d u c t = 3 2 - b i t A L U S h i f t r i g h t C o n t r o l P r o d u c t W r i t e t e s t 6 4 b i t s The trick is to use the lower half of the product to hold the multiplier during the operation. N o : < 3 2 r e p e t i t i o n s e p e t i t i o n ? Y e s : 3 2 r e p e t i t i o n s 10/5/2004 Comp 120 Fall 2004

What about the sign? Positive numbers are easy. How about negative numbers? 10/5/2004 Comp 120 Fall 2004

Faster Multiply See Booth coding in the book. A1 & B A0 & B A2 & B P32-P63 P2 P1 P0 P31 10/5/2004 Comp 120 Fall 2004

Division Start 1. Subtract Divisor from the Remainder leave the result in the Remainder >=0 <0 Test Remainder Restore Remainder by adding Divisor Shift Quotient to the left set its rightmost bit = 0 Shift Quotient to the left set its rightmost bit = 1 Shift Divisor Register right 1 bit Repeat 33 times 10/5/2004 Comp 120 Fall 2004