Chapter 2 : Data Representation

           Data Types

• Represented in binary-coded form.
•  Only have 0 & 1 to represent everything.

The Decimal Number System

·         The Base 10 number system uses the digit: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

                      

Example : The number 81 means eight tens plus one:

                                     81=(8*10) + 1

           The Binary Number System

•   A variable whose value may be either 0 or 1.
• Bits are organized into groups of 8 called bytes.
• Represented to the base 2

                   Example: 10₂ = ( 1 * 2¹ )  + ( 0 * 2⁰ ) = 2₁₀

             The Octal Number System

•  Base-8 number system
• Uses the digits 0, 1, 2, 3, 4, 5, 6, 7.

           The Hexadecimal Number System 

• The hexadecimal number system uses the following digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Number Conversion

 

Two’s complement benefit

•  One representation of zero
•  Arithmetic works easily
• Range for a word length of n bits :  -(2^n-1) à (2^n-1 – 1)

By     Kuan Wei Sern