Computer Architecture and Organization - Binary Multiplication - Booths Algorithm, Study notes of Computer Architecture and Organization

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Unit-2: Binary Multiplication-

Booth’s Algorithm

Recap

Session Objectives & Teaching Learning

Material

Session Plan

Introduction to Booth’s Algorithm

Flow Chart

Interpretation of example for signed multiplication

Example 

Assignment

References

OutLine

Session Objectives ◦ (^) To provide knowledge on Signed multiplications ◦ (^) To teach procedure for binary multiplication using Booth’s Algorithm ◦ (^) To solve the problems on Booth’s multiplication

Teaching Learning Material ◦ (^) LCD, White board Marker, Presentation slides Objectives & Teaching Learning Material

Session Plan Time (in min) Content Learning Aid and Methodology Faculty Approach Typical Student Activity Skill and Competency Developed

Re-Cap

Quiz Presentation Questions Organizes Answers Identifies Knowledge Evaluation

Binary

Multiplication

Explains Presentations Listens Knowledge

10 Algorithm Explains

Presentatio n

Observes Analytical

Interpretation of

an example to

algorithm

Explains

Presentatio n

Observes Analytical

15 Examples

Presentati

on

Facilitates Solves Analytical

Conclusion and Summary Summary Facilitates Listens Participates Comprehensio n

STARTSTART A 0 ; Q (^) -1 0 MMultiplicand Q Multiplier Countn A 0 ; Q (^) -1 0 MMultiplicand Q Multiplier Countn Q (^) 0 ,Q (^) - 1 Q (^) 0 ,Q (^) - 1 AA-M^ AA-M^ A A+MA A+M Arithmetic Shift right A, Q, Q- Count Count - Arithmetic Shift right A, Q, Q- Count Count - Count =0? Count =0? END END = 1 = 1 = 0 N0N0 Yes^ Yes = 1 = 1 = 0 = 0 Multiply 7 x 3 using above signed 2's compliment binary multiplication. Multiplicand =7  Binary equivalent is 0111 M Multiplier = 3  Binary equivalent is 0011 Q A Q Q-1 Action Count 0 0 0 0 0 0 1 1^0 Initial^4 1 0 0 1 0 0 1 1 0 AA-M 1 1 0 0 1 0 0 1 1 Shift 3 1 1 1 0 (^) 0 1 0 0 1 Shift 2 0 1 0 1 0 1 0 0 1 AA+M 0 0 1 0 1 0 1 0 0 Shift^1 0 0 0 1 0 1 0 1 0 Shift 0

-M

A

A

M

A

A

-7  Binary equivalent is 1001 -MM Step 1 2 2 3 4 4 5

Multiply the following using Booth’s

algorithm

7 x - -7 x 3 -7 x - 11 x 13 -11 x 13 11 x - -11 x -

Examples

Develop a Simulator to perform

multiplication operation two signed number

and display the step by step result.

Programming Assignment

Text Book

William Stallings “Computer Organization

and architecture” Prentice Hall, 7th edition,

References