1. October 15 Chapter 4 – Multiplication/Division Go to the State Fair!
2/21/2019
Comp 120 Fall 2001

2. Multiplication Facts N digit number TIMES a M digit number produces: ?
32 bit number TIMES a 32 bit number produces: ?
a (N+M) digit number
a 64 bit number
123
x 45
615
492
5535
101
x 11
1111
2/21/2019
Comp 120 Fall 2001

3. Multiplication: ImplementationS 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
2/21/2019
Comp 120 Fall 2001

4. Second Version 2/21/2019 Comp 120 Fall 2001 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
2/21/2019
Comp 120 Fall 2001

5. Example for second version
0010
Test true shift right 4
Test false shift right 3 2 1
1011
Initial
Product
Multiplicand
Multiplier
Step
Iteration
2/21/2019
Comp 120 Fall 2001

6. 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
2/21/2019
Comp 120 Fall 2001

7. What about the sign? Positive numbers are easy.
How about negative numbers?
2/21/2019
Comp 120 Fall 2001

8. 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
2/21/2019
Comp 120 Fall 2001