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COMPUTER ORGANIZATION
AND ASSEMBLY LANGUAGE
Lecture 10
Multiplication
Binary makes it easy
Multiplier bit = 0 place 0
Multiplier bit = 1 place multiplicand
(232-1)*(232-1) = 264 – 2.232 + 1 – need 64-bits
Multiplicand 1 0 0 0
Multiplier x 1 0 0 1
--------------
1 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
------------------
Product 1 0 0 1 0 0 0
Multiplication
Multiplicand 1 0 0 0
Multiplier x 1 0 0 1
--------------
1 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
------------------
Product 1 0 0 1 0 0 0
0 0 0 0 1 0 0 0 x 1 0 0 1
----------------------------------
0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-----------------------
0 1 0 0 1 0 0 0
Multiplicand
Product
Multiplier
64-bit ALU
64-bit
Control
Shift left Shift right
Add
Write
64-bit
Test
What should be
added in each step
Multiplication
0 0 0 0 1 0 0 0 x 1 0 0 1
-------------------------------------
0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-----------------------
0 1 0 0 1 0 0 0
8-bit
Control
Shift left Shift right
Add
Write
8-bit
Test
00001000 1001
00000000
1. Initialize
2. Test, Add, Write
00001000
3. Shift left multiplicand, shift right multiplier
00010000 0100
4. Test
5. Shift left multiplicand, shift right multiplier
00100000 0010
6. Test
7. Shift left multiplicand, shift right multiplier
01000000 0001
8. Test, Add, Write
9. Shift left multiplicand, shift right multiplier
01001000
100000004-bit
10. Done
0000
Multiply Algorithm 2
Multiplicand 1 0 0 0
Multiplier x 1 0 0 1
--------------
1 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
------------------
Product 1 0 0 1 0 0 0
1 0 0 0 x 1 0 0 1
------------------------------------
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0
-----------------------
0 1 0 0 1 0 0 0
Partial Product at
each step
Multiplicand
Product
Multiplier
32-bit ALU
32-bit
Control
Shift right
Add
Write
64-bit Shift right
Test
Multiply Algorithm 2
4-bit
Control
Shift right
Add
Write
8-bit
1 0 0 0 x 1 0 0 1
----------------------------
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0
-----------------------
0 1 0 0 1 0 0 0
Shift right
Test
4-bit
10011000
00000000
1. Initialize
2. Test, Add
3. Shift product right, shift multiplier right
10000000
4. Test
01000000
5. Shift product right, shift multiplier right
00100000
6. Test
00010000
7. Shift product right, shift multiplier right
10010000
8. Test, Add
9. Shift product right, shift multiplier right
01001000
10. Done
0100001000010000
Multiply Algorithm 2*
Multiplicand
32-bit ALU
32-bit
Control
Add
Write
64-bit
1 0 0 0 x 1 0 0 1
-------------------------------------
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0
-----------------------
0 1 0 0 1 0 0 0
Shift right
Multiplier Test
Multiplication
mult $rs, $rt Has 2 sources (32-bit registers)
No explicit destination Has 2 implicit destinations
$hi – upper 32-bits
$lo – lower 32-bits
Have to explicitly read these registers
mflo $rd Moves from $lo to $rd
mfhi $rd Moves from $hi to $rd
Also multu – un-signed multiply
Division
1001 Quotient
---------------
Divisor 1000 | 1001010
- 1000
-----------
10
101
1010
-1000
---------
10 Remainder
Divisor
Remainder
Quotient
64-bit ALU
64-bit
Control
Shift right Shift left
Subtract
Write
64-bit Test
32-bit
Divisor 1000 Quotient 1001
Dividend: 1001010
0001010
0001010
0001010
0000010 Remainder
Division
1001 Quotient
---------------
Divisor 1000 | 1001010
- 1000
-----------
10
101
1010
-1000
---------
10 Remainder
64-bit ALU
8-bit
Control
Shift right Shift left
Add/Sub
Write
8-bit Test
10000000
1. Initialize
0000
01001010
2. Subtract & test
5. Push 1 in quotient, shift divisor right
4-bit
6. Subtract & test
7. Restore remainder, push 0 in quotient, shift divisor right
8. Subtract & test
9. Restore remainder, push 0 in quotient, shift divisor right
10. Subtract & test
11. Push 1 in quotient, shift divisor right
11001010
3. Restore remainder, push 0 in quotient, shift divisor right
4. Subtract & test
12. Done
01001010
01000000
00001010
000100100000
1110101000001010
001000010000
1111101000001010
010000001000
00000010
100100000100
Division
div $rs, $rt
$lo = $rs/$rt; (has quotient)
$hi = $rs%$rt (has remainder)
Need mflo and mfhi
Transfer results of div to normal registers
divu
For unsigned division
Improved Division
Instead of shifting divisor right
Shift remainder to left
Use the least significant bits of remainder to store the
quotient
Divisor
32-bit ALU
32-bit
Control
Add
Write
64-bit Shift right
Remainder
