1. CSCI206 - Computer Organization & Programming
Integer Divide
zyBook: 10.4

2. Division: Similar to multiplication
Algorithm: subtract and shift...

3. Signed Division Same as signed multiply divide absolute values
resulting sign bit:
Quotient and remainder have the same sign

4. The Divider Same hardware as multiply! Setup
divisor in left half of divisor register (64 bit for now)
remainder register initialized with dividend in right half
e.g., would occupy

5. The Divider

6. 0111 / 0010 = ???? R ????
Example 1

7. 0111 / 0010 = 0011 R 0001
2’s comp of is
2’s comp of is
2’s comp of is
2’s comp of is
2’s comp of is

8. same as optimized multiply hardware
Optimized Divider
same as optimized multiply hardware
Algorithm
HI(Remainder) = 0
LO(Remainder) = Dividend
repeat N times:
Remainder <<= 1
HI(Remainder) -= Divisor
if HI(Remainder) > 0
Remainder[0] = 1
else
HI(Remainder) += Divisor
Remainder[0] = 0

9. Example with optimized divider
2’s comp 0010 = 1110
Iteration
Step
Divisor
Rem/Quotient
Initial values
0010 1
Rem << 1
HI(Rem) -= Div
Rem < 0, Rem+Div, Rem[0] = 0 2 3
Rem >= 0, Rem[0] = 1 4
Rem>=0, Rem[0] = 1
The values in read are quotient, the left part of Rem is the remainder.

10. Compared with hand-operation in decimal numbers
Remainder
00000
10970
10970
dividend
Quotient
______
23 |10970
_00476_
23 |10970
-092
0177
-161
0160
138 22
00000
10970
00023
divisor
00001
09700
00476
00001
09700
quotient
00010
97000
00022
remainder
00010
97000
00109
70000
00017
70004
109-4*23=17
00177
00040
00016
00047
177-7*23=16
00160
00470
Quotient
Remainder
00022
00476
160-6*23=22