1. CPS3340 Computer Architecture Fall Semester, 2013
Lecture 6: Binary Addition & Subtraction,
1-bit ALU
Instructor: Ashraf Yaseen
Department of Math & Computer Science
Central State University, Wilberforce, OH
09/17/2013

2. Review Last Class This Class Next Class Integrated Circuits
Decoder, Multiplexor
PLA, ROM
Don’t Care, Bus
This Class
Assignemnt2
Representation of Integer
Addition & Subtraction
1-bit ALU
Next Class
Quiz2
32-bit ALU

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
26 April, 2017
Integer Addition
§3.2 Addition and Subtraction
Example: 7 + 6
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. Arithmetic Logic Unit Arithmetic Logic Unit (ALU) Heart of a CPU
Operations
Arithmetic operations
Addition
Subtraction
Logical operations
NOT
AND OR

15. 1-bit Logical Unit for AND and OR

16. 1-bit adder

17. 1-bit adder truth table
can express the output functions Carry Out and Sum as logical equations, and these equations can in turn be implemented with logic gates

18. Simplifying 1-bit adder
If a and b and CarryIn are true, then the three other terms are true as well
can be simplified as
Values when CarryOut is true

19. Logic of CarryOut Bit

20. Logic of Sum Bit

21. Overall 1-bit ALU

22. Summary Bit, Byte, Word Binary Representation of Integer Addition
Subtraction
Overflow
1-bit ALU

23. What I want you to do Review Appendix C and Class Slides
Work on Assignment 2
Prepare for Quiz 2