1. Dr. Clincy Professor of CS
CS Chapter 2
Dr. Clincy
Professor of CS
Dr. Clincy
Lecture 4

2. Multiplication in base 2 – dealing with negative numbers
By hand – signed case – best to use 2’s complement
If both numbers are negative, perform as if both numbers are positive
If one is negative and one number is positive, see below – extend out left-most bit
Dr. Clincy
Dr. Clincy
Lecture 4
Lecture 2

3. How does the computer multiply integers (shifting) ?
Computer doesn’t actually multiply – it adds and shifts
Dr. Clincy
Dr. Clincy
Lecture 4
Lecture 3

4. Examples of Integer Multiplication by 2
Dr. Clincy
Dr. Clincy
Lecture 4 4 4

5. Another Example of Integer Multiplication by 2
Dr. Clincy
Dr. Clincy
Lecture 4 5 5

6. Examples of Integer Division by 2
Dr. Clincy
Dr. Clincy
Lecture 4 6 6

7. Booth’s Algorithm – Faster 2’s Complement Multiplication
Dr. Clincy
Dr. Clincy
Lecture 4 7

8. Booth’s Algorithm Concept
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Dr. Clincy
Lecture 4 8

9. Booth’s Algorithm Concept
Dr. Clincy
Dr. Clincy
Lecture 4 9

10. Booth’s Algorithm Standard Approach Booth’s Algorithm Approach
This is where 2’s complement comes into play
Dr. Clincy
Dr. Clincy
Lecture 4 10

11. Booth’s Algorithm
Only consider the first 16 bits – ignore beyond the 16th bit
Dr. Clincy
Dr. Clincy
Lecture 4 11

12. Character Codes
Calculations aren’t useful until their results can be displayed in a manner that is meaningful to people.
We also need to store the results of calculations, and provide a means for data input.
Thus, human-understandable characters must be converted to computer-understandable bit patterns using some sort of character encoding scheme.
Dr. Clincy
Lecture 4

13. Character Codes
Binary-coded decimal (BCD) was one of these early codes. It was used by IBM mainframes in the 1950s and 1960s.
In 1964, BCD was extended to an 8-bit code, Extended Binary-Coded Decimal Interchange Code (EBCDIC).
Until recently, ASCII was the dominant character code outside the IBM mainframe world.
Many of today’s systems embrace Unicode, a 16-bit system that can encode the characters of every language in the world
Dr. Clincy
Lecture 4

14. ASCII
Dr. Clincy
Lecture 4

15. EBCDIC
Dr. Clincy
Lecture 4

16. Character Codes
Calculations aren’t useful until their results can be displayed in a manner that is meaningful to people.
We also need to store the results of calculations, and provide a means for data input.
Thus, human-understandable characters must be converted to computer-understandable bit patterns using some sort of character encoding scheme.
Dr. Clincy
Lecture 4

17. Character Codes
Binary-coded decimal (BCD) was one of these early codes. It was used by IBM mainframes in the 1950s and 1960s.
In 1964, BCD was extended to an 8-bit code, Extended Binary-Coded Decimal Interchange Code (EBCDIC).
Until recently, ASCII was the dominant character code outside the IBM mainframe world.
Many of today’s systems embrace Unicode, a 16-bit system that can encode the characters of every language in the world
Dr. Clincy
Lecture 4