In this chapter you will learn about:

Non-positional number system 
Positional number system
Decimal number system
Binary number system
Octal number system
Hexadecimal number system
Convert a number’s base

Another base to decimal base

Decimal base to another base

Some base to another base

Shortcut methods for converting
Binary to octal number
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:

Non-positional 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 value-added 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 day-to-day 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 n-bit 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.