This document presents two algorithms for multiplication: multiplication of unsigned numbers and Booth's algorithm. It includes outlines, requirements, design choices, flowcharts and code demonstrations for each algorithm. The requirements are to write a program that takes decimal inputs, displays step-by-step traces, and does not crash on invalid inputs. The algorithms are implemented in C++ sequentially according to flowcharts. Booth's algorithm handles signed numbers using 2's complement representation.

1. MULTIPLICATION ALGORITHMS
Project of Option A
Code for Multiplication of unsigned numbers and Booth’s Algorithm
Presented by:
Saif Al Kalbani 39579
01-01-2014
ECCE6292
Special Topics in Computer
Engineering
Fall 2013
1
Sultan Qaboos University
College of Engineering
Department of Electrical and
Computer Engineering

2. Outline
2
 Introduction
 Requirements
 Design choices Selection
 Flowchart for multiplication of Unsigned
Numbers
 Flowchart for Booth’s algorithm
 Demo for Multiplication of unsigned Numbers
 Demo for Booth’s algorithm
 Conclusion

3. Requirement
3
 Selection of Multiplication/Devision Algorithm
 Write a program
 Input to be DECIMAL
 Display a trace of steps (As it was in the class)
 Must not crash on invalid inputs

4. Design
4
 Language
 C++
 Algorithm
 Multiplication of unsigned Numbers
 Booth’s Algorithm
 Sequential Development as per the flow chart
 Outputs of each stage was invistigated

5. FLOW CHART
Multiplication of Unsigned Numbers 5

6. Flow Chart
6
Request user for
Multiplicand
Check if
it is valid
input
Check if
it is
positive
Discard
input
NO NO

7. Flow Chart
7
Determine
the Size of
each
Initiate
arrays for
A, Q and M
Initialize A to
0’s

8. Flow Chart
8
Convert to
Boolean
Input that
to Q and M
Initiate the
Header

9. Flow Chart
9
Initialize C
Show the
initial value of
C,A,Q and M
Initiate the
Counter

10. Flow Chart
10
Chec
k Qo
Add
A,M
Show
the
results
Shift
C,A,Q
Show
the
results
YE
S
NO

11. Flow Chart
11
Check
the
counter
if 0
Show the results END
Chec
k Qo

12. Flow Chart
12
Start
C,A  0
M  Multiplicand
Q  Multiplier
Count  n
Q0=1?
C,A  A+M
Shift C,A,Q
Count  Count-1
Count=0
?
END
NO
YE
S
NO
YE
S

13. FLOW CHART
Booth’s Algorithm 13

14. Flow Chart
14
Request user for
Multiplicand
Check if
it is valid
input
Check if
it is
positive
Discard
input
NO
Put signs
in registers
Convert to
Positive
NO

15. Flow Chart
15
Determine
the Size of
each
Initiate
arrays for A,
Q and M
Initialize
A,Q,M to 0’s

16. Flow Chart
16
Convert to
Boolean
Check
sign=0
Input that to Q
and M
Initiate the
Header
Convert to
2’s
complement
NO

17. Flow Chart
17
Initialize Q-1
Show the initial
value of A,Q,Q-1
and M
Initiate the
Counter

18. Flow Chart
18
Check
Qo,Q-
1
Add
A,M
Show
the
results
Shift
A,Q,Q-1
Show
the
results
01
00 OR 11
Sub A,M
(Add A,-
M)

19. Flow Chart
19
Check
the
counter
if 0
Show the results END
Chec
k
Qo,Q-
1

20. Flow Chart
20
Start
Q-1,A  0
M  Multiplicand
Q  Multiplier
Count  n
Q0,Q-1=?
A  A+M
Arithmetic
ShiftA,Q,Q-1
Count  Count-1
Count=0
?
END
11 OR 00
01
NO
YE
S
A  A-M
10

21. Conclusion
21
 Multiplication Algorithms Program Developed
 Checks to avoid Crash
 Arrays for the operands and others
 Functions for Efficiency
 Loops for Manipulation and Show

22. Thank You
Q&A22