1) The document describes the process of multiplying two unsigned binary integers using a block diagram and flowchart. It involves generating partial products, shifting and adding them to get the final product. 2) An example multiplication of 10112 x 11012 is shown step-by-step to illustrate the process. Partial products are generated and shifted before being added. 3) The result of multiplying 10112 x 11012 is calculated to be 1000111112 or 14310 in decimal.

1. Multiplication of Unsigned Binary Integer
Presented by:
Name: Zubayer Farazi
Presented for:
Md. Mostafiz Ahammed
Lecturer
Department of CSE,
Notre Dame University, Bangladesh
Department of Computer Science and Engineering

2. Outline
1
 Introduction of Multiplication
 Example of Multiplication
 Block Diagram
 Flowchart
 Reference

3. Multiplication
 Compared with addition and subtraction, multiplication is a
complex operation , whether performed in hardware or
software.
 Multiplication involves the generation of partial products, one
for each digit in the multiplier.
 These partial products are then summed to produce the final
product.
2

4. Multiplication
Example:
1 0 1 1
1 1 0 1
Multiplicand
Multiplier
1 0 1 1
0 0 0 0
1 0 1 1
1 0 1 1
1 0 0 0 1 1 1 1
Partial Product
3
Product

5. Block Diagram
Mn-1 … M₀
N-bit Adder
An-1 … A₀
Shift and Control logic
C
Qn-1 … Q₀
Multiplicand
Multiplier
Register
Add
4

6. Flowchart Start
Shift right C,A,Q
C,A 0
N N-1
Yes
End
Q=1?
M Multiplicand
Q Multiplier
C,A 0
Yes
C,A A + M
No
No
N=0? 5

7. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
4
6
1 0 1 1 1 1 0 1 = ?
*

8. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
4
3
0 0 0 0
1 0 1 1
1 0 1 1
A
M
A
7
1 0 1 1 1 1 0 1 = ?
*

9. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
Discard
8
1 0 1 1 1 1 0 1 = ?
*

10. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 Shift right C, A, Q
0
4
3
2
0
10
1 0 1 1 1 1 0 1 = ?
*

11. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
2
11
1 0 1 1 1 1 0 1 = ?
*

12. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
2 Shift right C, A, Q
Discard
12
1 0 1 1 1 1 0 1 = ?
*

13. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
2
1
Shift right C, A, Q
13
1 0 1 1 1 1 0 1 = ?
*

14. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
1 1 0 1 1 1 1 1 Add A with A:
A=A+M
2
1
0 0 1 0
1 0 1 1
1 1 0 1
A
M
Shift right C, A, Q
A
0
14
1 0 1 1 1 1 0 1 = ?
*

15. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
1 1 0 1
0 1 1 0
1 1 1 1
1 1 1 1
Add A with A:
A=A+M
Shift right C, A, Q
2
1
Shift right C, A, Q
0
Discard
0
15
1 0 1 1 1 1 0 1 = ?
*

16. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
1 1 0 1
0 1 1 0
1 1 1 1
1 1 1 1
Add A with A:
A=A+M
Shift right C, A, Q
2
1
0
16
1 0 1 1 1 1 0 1 = ?
*

17. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
1 1 0 1
0 1 1 0
1 1 1 1
1 1 1 1
Add A with A:
A=A+M
Shift right C, A, Q
2
1
0 0 0 1 1 1 1 1
1 Add A with A:
A=A+M
0 1 1 0
1 0 1 1
1 0 0 0 1
A
M
A
0
0
17
0

18. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
1 1 0 1
0 1 1 0
1 1 1 1
1 1 1 1
Add A with A:
A=A+M
Shift right C, A, Q
2
1
0 0 0 1 1 1 1 1
1 Add A with A:
A=A+M
1 0 0 0 1 1 1 1 Shift right C, A, Q
0
Discard 18
0

19. Start
Yes
Shift right C,A,Q
C,A 0
N N-1
Yes
End
M Multiplicand
Q Multiplier
C,A 0
Q=1?
C,A A + M
No
No
N=0?
N M C A Q Comments
1 0 1 1 0 0 0 0 0 1 1 0 1 Initialization
1 0 1 1
0 1 1 0 1
Add A with A:
A=A+M
0 1 0 1 1 1 1 0 Shift right C, A, Q
0
4
3
0 0 1 0 1 1 1 1
0
1 1 0 1
0 1 1 0
1 1 1 1
1 1 1 1
Add A with A:
A=A+M
Shift right C, A, Q
2
1
0 0 0 1 1 1 1 1
1 Add A with A:
A=A+M
1 0 0 0 1 1 1 1 Shift right C, A, Q
0
0
1 0 1 1
1 0 1 1
1 0 1 1
1 0 1 1
The Result is : (010001111) ₂ = 143₁₀ 19
*
1 0 1 1 1 1 0 1 = ?

20. Reference
 Class lecture sheet
https://classroom.google.com/u/1/c/NTQ2OTc1NTQ0MzI3
/m/NTA3NTUwNDg3Mjkx/details
20

21. Thank You