In this chapter you will learn about:
Decimal number system
Binary number system
Octal number system
Hexadecimal number system
Another base to decimal base
Decimal base to another base
Some base to another base
Octal to binary number
Binary to hexadecimal number
Hexadecimal to binary number
Fractional numbers in the binary number system
Two types of number systems are:
Nonpositional number systems
Positional number systems
Characteristics
Use symbols like I for one, II for 2, III for 3, IIII
for 4, IIIII for five, etc
Each image represents a similar worth despite its position within the variety
The symbols are merely valueadded to search out out the worth of a specific variety
Difficult
It is difficult to perform arithmetic with such a number system.
Characteristics
Use only a few symbols called digits
These symbols represent different values depending on the position they occupy in the number
The value of each digit is determined by
1. Thedigititself
2. Thepositionofthedigitinthenumber
3. Thebaseofthenumbersystem
(base = total number of digits in the number system)
The maximum value of a single digit is always equal to one less than the value of the base
Characteristics

A positional number system

Has10symbolsordigits(0,1,2,3,4,5,6,7, 8, 9). Hence, its base = 10

The maximum value of a single digit is 9 (one less than the value of the base)

Each position of a digit represents a specific power of the base (10)

ß We use this number system in our daytoday life
Characteristics

A positional number system

It has only 2 symbols or digits (0 and 1). Hence its base = 2

The maximum value of a single digit is 1 (one less than the value of the base)

Each position of a digit represents a specific power of the base (2)

This number system is used in computers
Representing Numbers in Different Number Systems
In order to be specific about which number system we are referring to, it is a common practice to indicate the base as a subscript. Thus, we write:
Bit
Bit stands for binary digit
A bit in computer terminology means either a 0 or a 1
A binary number consisting of n bits is called an nbit number
Octal Number System
Characteristics
 A point mathematical notation
Has total eight symbols or digits (0, 1, 2, 3, 4, 5, 6, 7).  Hence, its base = eight
 The maximum price of one digit is seven (one but the worth of the bottom
 Each position of a digit represents a selected power of the bottom (8)
 Since there are solely eight digits, three bits (23 = 8) are ample to represent any positional representation system range in binary.
Hexadecimal Number System
Characteristics
 A point numeration system
Has total sixteen symbols or digits (0, 1, 2, 3, 4, 5, 6, 7,
8,9,A,B,C,D,E,F). Henceitsbase=16  The symbols A, B, C, D, E, and F represent the decimal values ten, 11, 12, 13, fourteen and fifteen severally
 The maximum price of one digit is fifteen (one but the worth of the base)
 Each position of a digit represents a specific power of the base (16)
 Since there are only 16 digits, 4 bits (24 = 16) are sufficient to represent any hexadecimal number in binary.