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.
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Booth algorithm
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
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
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