1. Lecture 5 Multiplication and Division
ECE 0142 Computer Organization
Lecture 5 Multiplication and Division

2. Recitation
Multiplying two numbers in 2’s complement, using the best hardware we learned (pp. 25)
11010  0101
0101  11010

3. Recitation (Implementation 3)
Let’s do x 0101 (-6 x 5 = -30)
Iteration
Implementation 3
Step
Multiplier
Multiplicand
Product|Multiplier
initial values
0101
11010 1
1: 1 -> product = product + multiplicand
2: Multiplier shift right/ Product shift right
×010 2
1: 0 -> no op
××01 3
×××0 4
××××

4. Recitation (Implementation 3)
Let’s do 0101 x (5 x -6 = -30)
Iteration
Implementation 3
Step
Multiplier
Multiplicand
Product|Multiplier
initial values
11010
0101 1
1: 0 -> no op
2: Multiplier shift right/ Product shift right
×1101 2
1: 1 -> product = product + multiplicand
××110 3
×××11 4
××××1 5
1: 1 -> product = product - multiplicand
××××1
0101
2: Multiplier shift right/ Product shift right
×××××

5. Use Booth Alg.
Solve 

6. Booth’s Algorithm Example
Let’s do 0110 x (6 x -3)
Iteration
Implementation 3
Step
Multiplicand
Product
initial values
0110 1
00 -> no op
shift right 2 3 4
10 -> product = product – multiplicand 5
11 -> no op
0110
shift right 6
11 -> no op
0110
shift right 7
00 -> no op
0110
shift right