# Decimal Number

Topics: Hexadecimal, Binary numeral system, Decimal Pages: 9 (1676 words) Published: October 30, 2013
﻿ NUMBER SYSTEM
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.

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

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....