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### In this chapter you will learn about:

Non-positional number system
Positional number system
Decimal number system
Binary number system
Octal 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
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

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### 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

### 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. ### 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.  