1. CHAPTER 9 COMPUTER ARITHMETIC - ALU
CSNB123 coMPUTER oRGANIZATION
NSMS2013 Ver.1
Systems and Networking

2. Overview NSMS2013 Ver.1 Systems and Networking
Arithmetic Logic Unit (ALU)
Focus on – computer arithmetic
Logic function
Support 2 types of number
Integer
Floating-point
Component in processor
NSMS2013 Ver.1
Systems and Networking

3. ALU
Part of the computer that do the arithmetic and logical operation on data
Simple digital logic devices that can;
Store binary digits
Perform simple BOOLEAN logic operations
CPU
Registers
Arithmetic Logic Unit (ALU)
Internal CPU Interconnection
Control Unit
NSMS2013 Ver.1
Systems and Networking

4. Systems and Networking
ALU Interconnection
NSMS2013 Ver.1
Systems and Networking

5. ALU and Registers CPU Component Description Registers
Present data to ALU
Store result of an operation
Temporary storage locations within the processor that are connected by signal paths to the ALU
ALU set flags – result of an operation – store in registers
Control unit
Provides signals that control;
Operation of the ALU
Movement of the data into and out of the ALU
CPU
Registers
Arithmetic Logic Unit (ALU)
Internal CPU Interconnection
Control Unit
NSMS2013 Ver.1
Systems and Networking

6. Integer Representation
Computer - logic circuits - operate on information; 0 and 1  two values electrical signals – bit
How to represent negative value in binary?
Sign-magnitude representation
Twos complements representation
NSMS2013 Ver.1
Systems and Networking

7. Sign Magnitude Representation
NSMS2013 Ver.1
Systems and Networking

8. Sign-magnitude Representation
Ways of presenting -ve and +ve integers
The most significant (leftmost) bits in the word as a sign bit
Example: if the sign bit is 0 then the number is +ve, vice versa
Hence sign magnitude representation employed sign bit
NSMS2013 Ver.1
Systems and Networking

9. Sign-magnitude Representation (Cont.)
Example
+18 =
-18 =
Rarely used
Drawbacks;
Addition/subtraction require a consideration of both the signs of the numbers and their relative magnitudes to carry out the required operation
2 representation of 0;
+010 =
-010 =
NSMS2013 Ver.1
Systems and Networking

10. Twos complements representation
NSMS2013 Ver.1
Systems and Networking

11. Twos Complements Representation
Used the most significant bit (MSB) as a sign bit (similar to sign magnitude)
Differs – the other bits are interpreted
Example:
+3 =
+2 =
+1 =
+0 =
NSMS2013 Ver.1
Systems and Networking

12. Twos Complements Representation (Cont.)
Negative – sign bit = 1
Example:
-1 =
-2 =
-3 =
NSMS2013 Ver.1
Systems and Networking

13. Twos Complements Representation (Cont.)
Steps for negative integers. Example: -3
+3 = 1
Step 1: Take +ve value
Step 2: Boolean Complement
Step 3: Add 1 to LSB
Result
NSMS2013 Ver.1
Systems and Networking

14. Twos Complements Representation (Cont.)
Example: 1
= 16
-16
Step 1: Take value
Step 2: Boolean Complement
Step 3: Add 1 to LSB
Result
Convert into decimal
Put –ve sign
NSMS2013 Ver.1
Systems and Networking

15. Twos Complements Representation – Special Case
Example: 0, consider an 8-bit representation 1
Step 1: Take value
Step 2: Boolean Complement
Step 3: Add 1 to LSB
Result
1 carry out at most significant bit (MSB)
- Ignored hence -0 = 0
NSMS2013 Ver.1
Systems and Networking

16. Twos Complements Representation – Range of Numbers
8-bit 2s complement
+127 =
-127 =
16-bit 2s complement = =
NSMS2013 Ver.1
Systems and Networking

17. Twos Complements Representation – Conversion between lengths
Positive
Negative
Pack with leading zeros
8-bits
+18 =
16-bits
-18 =
Pack with leading ones
8-bits
+18 =
16-bits
-18 =
NSMS2013 Ver.1
Systems and Networking

18. Twos Complements Representation - Operations
Addition
Subtraction
NSMS2013 Ver.1
Systems and Networking

19. Twos Complements Representation - Operations
Addition
Addition follows as if the two numbers were unsigned integers (positive or zero)
Overflow – result is larger than word
ALU provide signals
NSMS2013 Ver.1
Systems and Networking

20. Twos Complements Representation - Operations
Subtraction
Do subtraction via addition
NSMS2013 Ver.1
Systems and Networking

21. Twos Complements Representation - Operations
OVERFLOW RULE
If two numbers are added, and they BOTH are POSITIVE or BOTH NEGATIVE,
Then OVERFLOW occurs if and only if the RESULT has the OPPOSITE SIGN
NSMS2013 Ver.1
Systems and Networking