# Decimal Number

**Topics:**Hexadecimal, Binary numeral system, Decimal

**Pages:**9 (1676 words)

**Published:**October 30, 2013

Definition

It defines how a number can be represented using distinct symbols. A number can be represented differently in different systems, for instance the two number systems (2A) base 16 and (52) base 8 both refer to the same quantity though the representations are different.

When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number. A value of each digit in a number can be determined using

The digit

The position of the digit in the number

The base of the number system (where base is defined as the total number of digits available in the number system).

1. Decimal Number System

The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands and so on. Each position represents a specific power of the base (10). For example, the decimal number 1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds position, and 1 in the thousands position, and its value can be written as (1x1000)+ (2x100)+ (3x10)+ (4xl)

(1x103)+ (2x102)+ (3x101)+ (4xl00)

1000 + 200 + 30 + 1

1234

As a learner you should understand the following number systems which are frequently used in computers. S.N.

Number System & Description

1

Binary Number System

Base 2. Digits used: 0, 1

2

Octal Number System

Base 8. Digits used: 0 to 7

4

Hexa -Decimal Number System

Base 16. Digits used: 0 to 9, Letters used: A- F

2. Binary Number System

Characteristics

Uses two digits, 0 and 1.

Also called base 2 number system

Each position in a binary number represents a 0 power of the base (2). Example 20 Last position in a binary number represents a x power of the base (2). Example 2x where x represents the last position - 1. Example

Binary Number: 101012

Calculating Decimal Equivalent:

Step

Binary Number

Decimal Number

Step 1

101012

((1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10

Step 2

101012

(16 + 0 + 4 + 0 + 1)10

Step 3

101012

2110

Note that: 101012 is normally written as 10101.

3. Octal Number System

Characteristics

Uses eight digits, 0,1,2,3,4,5,6,7.

Also called base 8 number system

Each position in a octal number represents a 0 power of the base (8). Example 80 Last position in a octal number represents a x power of the base (8). Example 8x where x represents the last position - 1. Example

Octal Number: 125708

Calculating Decimal Equivalent:

Step

Octal Number

Decimal Number

Step 1

125708

((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10

Step 2

125708

(4096 + 1024 + 320 + 56 + 0)10

Step 3

125708

549610

Note that 125708 is normally written as 12570.

4. Hexadecimal Number System

Characteristics

a. Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. b. Letters represents numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15. c. Also called base 16 number system

d. Each position in a hexadecimal number represents a 0 power of the base (16). Example 160 e. Last position in a hexadecimal number represents a x power of the base (16). Example 16x where x represents the last position - 1. Example

Hexadecimal Number: 19FDE16

Calculating Decimal Equivalent:

Step

Binary Number

Decimal Number

Step 1

19FDE16

((1 x 164) + (9 x 163) + (F x 162) + (D x 161) + (E x 160))10 Step 2

19FDE16

((1 x 164) + (9 x 163) + (15 x 162) + (13 x 161) + (14 x 160))10 Step 3

19FDE16

(65536+ 36864 + 3840 + 208 + 14)10

Step 4

19FDE16

10646210

They also include:

Natural numbers

The counting numbers (1, 2, 3,4,5 ...), are called natural numbers....

Please join StudyMode to read the full document