Number system in ICT

Number system in ICT

In information and communication technology various number systems are used, they are essential for data representation, processing, Communication etc.The whole computer system is based upon these number system, they are the foundation of ICT. That enables easy conversation of numbers for technical purpose. A strong understanding of these number system is very important for anyone working in field of ICT. The primary number system in ICT include:

1) Positional number system

In a positional number system, the value of a digit depends on its Position within the number. The most common examples of Positional number system are binary, octal, decimal and hexadecimal systems. And in non Positional number system value of each digit does not depend on its position within the number.

An example of a non-positional number system is Roman numerals, where specific letters like 'I' for 1, 'V' for 5, 'X' for 10, etc.

1)BINARY NUMBER SYSTEM (Base-2)

Binary number system is Base-2 number system because it uses only two digits 0 and 1. Each position in a binary number represents a 'n' power of base 2.

BIT OR BINARY UNIT

Unit of measurement in binary system is bit or binary digit. It is smallest unit of digital information in computer. It can hold one of two values 0 or 1.

BYTE

A byte is a fundamental unit of digital information storage and processing in computing. It consists of 8 binary bits, each of which can have a value of 0 or 1. 

Collection of 4 bits are called one nibble.

1)Byte=                      8 Bits

2)1 kilobyte=           1024 bytes

3)1 megabyte =       1024 kilobytes

4)1 Gigabyte =         1024 megabytes

5)1 Terabyte =         1024 Gigabytes

6)1 Petabyte=          1024 terabytes

2)OCTAL NUMBER SYSTEM

The octal number system is a base-8 numeral system. In contrast to the more common decimal system (base-10) and the binary system (base-2), which uses two digits (0 and 1), the octal system uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.Each digit in an octal number represents a power of 8.

3)DECIMAL NUMBER SYSTEM

The decimal number system, also known as the base-10 system, it is the most common way of representing numbers. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit represents a specific value, and the position of a digit in a number determines its place value.

4) HEXADECIMAL NUMBER SYSTEM

The hexadecimal number system, often referred to as "hex," is a base-16 numbering system. It uses 16 distinct symbols to represent values: the regular decimal digits (0-9) and six additional symbols (usually A, B, C, D, E, and F) to represent values 10 to 15. In the hexadecimal system, each digits position has a place value, similar to the decimal system.

NUMBER SYSTEM CONVERSION

1)From Decimal to Binary

Example 1: Convert  (143)₁₀  to Binary

Step 1: Start with Decimal number

Step 2: Divide 143 by 2 and write down the remainder (0 or 1)

Step 3: Continue dividing the quotient from the previous step by 2 and writing down the remainders until the quotient becomes 0

Step 4: When you reach a quotient of 0, stop. The binary representation is the sequence of remainders read from bottom to top.

143/2=71 with remainder is 1

71/2=35 with remainder is 1

35/2=17 with remainder is 1

17/2= 8 with remainder is 1

8/2= 4 with remainder is 0

4/2= 2 with remainder is 0

1/2=0 with remainder is 1

So (143)₁₀in binary form is 1001111

Example 2: Convert (416)₁₀to binary

416/2=208  with remainder 0

208/2=104  with remainder 0

104/2=52  with remainder 0

52/2=26 with remainder 0

26/2=13 with remainder 0

13/2=6  with remainder 1

6/2=3  with remainder 0

3/2=1 with remainder 1

1/2=0 with remainder 1

So (416)₁₀  binary form is 110100000

2) From Binary to Decimal

Example 1: Convert 10110 to Decimal

Step 1: write down the binary number 10110

Step 2: Multiply each digit of binary number by the power of two

Step 3: Simplify the Powers

1x2⁴+0x2³+1x2²+1x2¹+0x2⁰

^{1x16+0x8+1x4+1x2+0x2}

16+0+4+2+0

10110= (22)₁₀

So (22)₁₀  is the Decimal equivalent of binary number 10110.

Example 2: Convert  1101 to Decimal

1x2³+1x2²+0x2¹+1x2⁰

1x8+1x4+0x2+1x1

8+4+0+1 =13

1101=(13)₁₀

So (13)₁₀ is the Decimal equivalent of binary number 1101

3) Convert from Decimal to Octal

Example 1: Convert(150)₁₀ to Octal

Step 1: Divide(150)₁₀  by 8 untill the quotient is 0

150/8=18 with remainder 6

18/8=2 with remainder 2

2/8=0 with remainder 2

Step 2: Read from bottom to top as 226

So (226)8 is the octal equivalent to Decimal number (150)₁₀

Example 2: Convert (325)₁₀ to Octal

325/8=40 with remainder 5

40/8= 5 with remainder 0

5/8= 0 with remainder 5

So (505)8is the octal equivalent to Decimal number (325)₁₀ 

4)Octal to Decimal

Example 1: Convert (147)8Octal to Decimal

Multiply each digits of octal number by corresponding power of 8

1x8²+4x8¹+7x8⁰

1x64+4x8+7x1

64+32+7=103

So (103)₁₀is decimal equivalent of the octal number (147)8

Example 2 Convert (1116)8  to Decimal

1x8³+1x8²+1x8¹+6x8⁰

1x512+1x64+1x8+6x1

512+64+8+6=590

So  (590)₁₀is decimal equivalent of the octal number (1116)8

5) Decimal to hexadecimal

Example 1: Convert (601)₁₀  to hexadecimal

 Divide (601)₁₀ by 16 until quotient is 0

601/16=37 with remainder 9

37/16=2 with remainder 5

2/16=0 with remainder 2

So (601)₁₀ in hexadecimal form is (259)₁₆

Example 2: Convert (1024)₁₀ to hexadecimal

1024/16=64 remainder 0

64/16=4 remainder 0

4/16=0 remainder 4

So (1024)₁₀ in hexadecimal systems is (400)₁₆

Hexadecimal to Decimal

Example1: Convert A2B16to Decimal

A2B16 = (A × 162) + (2 × 161) + (B × 160)

= (A × 256) + (2 × 16) + (B × 1)

= (10 ×256) + 32 + 11

= 2560 + 43

=2603

So A2B16 in decimal form is (2603)₁₀