1

MULTIPLICATION ALGORITHMS

Project of Option ACode for Multiplication of unsigned numbers and Booth’s Algorithm

Presented by:Saif Al Kalbani 39579

01-01-2014

ECCE6292Special Topics in Computer EngineeringFall 2013

Sultan Qaboos UniversityCollege of Engineering

Department of Electrical and Computer Engineering

2

Outline

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

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

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

6

Flow Chart

Request

user for

Multiplicand

Check if it is valid inpu

t

Check if it is positive

Discardinput

NO NO

7

Flow Chart

Determin

e the Size of

each

Initiate

arrays for A, Q and M

Initialize A to 0’s

8

Flow Chart

Convert to

Boolean

Input

that to Q and M

Initiate the Header

9

Flow Chart

Initialize C

Show the

initial value

of C,A,Q and M

Initiate the Counter

10

Flow Chart

Check Qo

Add A,M

Show the results

Shift C,A,Q

Show the results

YES

NO

11

Flow Chart

Check the counter if 0

Show the results

END

Check Qo

12

Flow Chart

StartC,A 0

M MultiplicandQ Multiplier

Count n

Q0=1?

C,A A+M

Shift C,A,QCount Count-1

Count=0?

END

NOYES

NO

YES

13

FLOW CHART

Booth’s Algorithm

14

Flow Chart

Request

user for

Multiplicand

Check if it is valid inpu

t

Check if it is positiveDiscard

input

NO

Put signs in

registers

Convert to Positive

NO

15

Flow Chart

Determin

e the Size of

each

Initiate

arrays for A, Q and M

Initialize

A,Q,M to 0’s

16

Flow Chart

Convert to Boolean

Check

sign=0

Input that to Q and M

Initiate

the Header

Convert to 2’s

complement

NO

17

Flow Chart

Initialize Q-1

Show the

initial value of A,Q,Q-1 and M

Initiate the Counter

18

Flow Chart

CheckQo,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)

10

19

Flow Chart

Check the counter if 0

Show the results

END

Check

Qo,Q

-1

20

Flow Chart

StartQ-1,A 0

M MultiplicandQ 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

YES

A A-M

10

21

Conclusion

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&A