1. Integer Real Numbers Character Boolean Memory Address CPU Data Types
Chapter 3
Integer
Real Numbers
Character
Boolean
Memory Address

2. Integer Integer Whole numbers No decimal places Unsigned integers
Use entire by ( 8 or 6 bits) for number
Lowest number is zero (0)
Signed integers
Use high order bit for + or – sign
Octal machines have 5 bits for number (out of 6) Excess notation
Hex machines have 7 bit for number (out of 8) Excess notation

3. Octal Integer 6 BIT number X X X X X X Weight value 32 16 8 4 2 1
All positions = “1” (“ON”)
Not counted: used for sign
Unsigned
Signed

4. Hexadecimal Integer 8 BIT number X X X X X X X X
Weight value
All positions = “1” (“ON”)
Not counted: used for sign
Unsigned
Signed

5. Arithmetic Operations
Addition
Subtraction
Multiplication
Division

6. Add two numbers Addition Decimal Binary Binary bit weights=

7. Subtract two numbers Subtraction ? Answer is: 6 - 5 ----- 0
Decimal Binary Binary bit weights
= * ? 1 2 3 4
Borrow 1 from 2s position add to 1s position
Subtract 1s position
Subtract 2s position 5 6 7
Answer is:
Subtract 4s position
Subtract 8s position

8. Complements Binary numbering scheme Ones (1) become zero (0)
Zeros (0) become ones (1)
Octal Hexadecimal
0 000 = = = = = = = = = = = = = = = = = = A = B = C = D = E = F = 0000

9. Computers MULTIPLY, SUBTRACT and DIVIDE by ADDITION
Two’s Complement
Computers MULTIPLY, SUBTRACT and DIVIDE by ADDITION
Binary numbering scheme
Used to work with negative numbers
Ones (1) become zero (0)
Zeros (0) become ones (1)
Data is signed if:
Variable data type was defined as signed in the program
The number is converted in the program
The computer does a Subtract or Divide
Formula for conversion
Original binary number
Compliment the number
Ones to Zeros
Zeros to Ones
Add binary one to lowest position
High order carry's are discarded

10. Add two numbers Two’s Complement Decimal Binary Binary bit weights=

11. * Two’s Compliment of 5 Subtract two numbers Two’s Complement
Decimal Binary Binary bit weights
= *
* Two’s Compliment of 5
5 = Original
Compliment Add one Two’s compliment 1011

12. Subtraction Division Addition and Two’s Compliment Summary
Computers do
Subtraction
And
Division
Using
Addition and Two’s Compliment