1. Computer Architecture & Operations I
Instructor: Yaohang Li

2. Review Last Class This Class Next Class Integrated Circuits Decoder
Multiplexor
PLA
ROM
Don’t Care
Bus
This Class
Representation of Integer
Addition
Subtraction
Next Class
Design of ALU
Assignment 2

3. Bit, Byte, and Word 1 Bit – 0 or 1 1 Byte – 8 bits
1 Word – N bytes (in general)
4 bytes in a word (in our book)

4. Most Significant Bit and Least Significant Bit
Most Significant Bit (High-Order Bit)
The bit position having the greatest value
Usually the left-most bit
Least Significant Bit (Low-Order Bit)
The bit position having the smallest value
Usually the right-most bit

5. Binary Representation of Decimal Number
Using a binary number to represent a decimal number
Example
What is the maximum number a byte can represent?
Binary  1
Decimal 
1×210 +
0×29 +
0×28 +
1×27 +
0×26 +
1×25 +
0×24 +
1×23 +
1×22 +
0×21 +
1×20 =
1197

6. Binary Representation of Integers
Unsigned Integers
0 and positive integers only
Signed Integers
0, negative, and positive integers
Three ways
Sign-Magnitude
1’s Complement
2’s Complement

7. Unsigned Integers Unsigned Integers Example Consider a word = 4 bytes
Can represent numbers from 0 to
Decimal:
0 to 232-1
Binary:
0 to
Example =

8. Signed Integer – Sign Magnitude
Use the most significant bit of the word to represent the sign
0 – Positive
1 – Negative
Rest of the number is encoded in magnitude part
Example = =
Two representations of 0
0 =
-0 =
Cumbersome in Arithmetic

9. 1’s Complement 1’s Complement
Negative number is stored as bit-wise complement of corresponding positive number
Use the most significant bit of the word to represent the sign
0 – Positive
1 – Negative
Example = =
Still two representations of zero
0 =
-0 =

10. 2’s Complement 2’s Complement
Positive number represented in the same way as sign-magnitude and 1’s complement
Negative number obtained by taking 1’s complement of positive number and adding 1 =
1’s comp: =
2’s comp: =
One version of 0
Convenient in arithmetic

11. Morgan Kaufmann Publishers
17 April, 2018
Integer Addition
Example: 7 + 6
§3.2 Addition and Subtraction
Chapter 3 — Arithmetic for Computers

12. Integer Subtraction Subtraction is actually an addition
Example: 7 – 6 = 7 + (-6)
2’s complement

13. Overflow Overflow if result out of range
Adding +value and –value operands, no overflow
Adding two +value operands
Overflow if result sign is 1
Adding two –value operands
Overflow if result sign is 0

14. Summary Bit, Byte, Word Binary Representation of Integer Addition
Subtraction
Overflow

15. What I want you to do
Review Appendix B