1. CSCI206 - Computer Organization & Programming
Integer Multiplication
zyBook: 10.3

2. 2’s Complement Multiplication
For powers of 2, multiply is trivial (shift left).
else use elementary algorithm:

3. Algorithm
In general, multiplying a M bit number times a N bit number results in M + N bits
multiplicand
multiplier
product = 0
for i in range(0, N):
if multiplier[i] == 1:
product += multiplicand << i
product

4. Signed Multiplication
This algorithm works for unsigned numbers.
For signed numbers, multiply the absolute values and then add the proper sign to the result.

5. Signed Multiplication
Resulting sign is
+ x + = +
+ x - = -
- x + = -
- x - = +
In general:
xor of input sign bits to get resulting sign bit

6. The Multiplier
multiplicand
x multiplier
Setup
multiplicand in lower half of multiplicand register (2n bits)
multiplier in multiplier register (n bits)
product register is zero (2n bits)

7. The Multiplier

8. 0010 x 0011 = ????
Example 1

9. 0010 x 0011 = 0110

10. Product is the MIPS hi/lo registers
Optimized Multiplier
Product is the MIPS hi/lo registers
Multiplier is initialized in the left half of the product register. Now we shift product register right. The multiplicand is 32-bits and not shifted because the result is written to the correct position in the product register after 32 right shifts.