CSCI206 - Computer Organization & Programming

1. CSCI206 - Computer Organization & Programming Integer Multiplication Revised by Alexander Fuchsberger and Xiannong Meng in spring 2019 based on the notes by other instructors. 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 = 0; i < N; i ++) { if (multiplier[i] == 1) // shift m by i bits then add // m remains the same! product += multiplicand << i; product Demo mult.c

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 1011 multiplicand x 1110 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. Optimized Multiplier Basic circuits 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. Product is the MIPS hi/lo registers Optimized one