Number System Conversion

Number System Conversion




Number System is way of representing the numbers across various domain and technology fields. Number system is mainly consists of following number formats:

  • Binary Numbers: consists of 1’s and 0’s and is known as base 2.
  • Decimal Numbers: consists of normal readable digits and is also known as base 10.
  • Hexadecimal Numbers: consists of numbers from 0-9 and alphanumeric representation from A-F. It is also known as base 16.
  • Octal Numbers: consists of number from 0-8 and is also known as base 8.

Base informs about the number of numeric digits used in any format of number system

Each of the number formats has its own usage and representation.

Binary Numbers: They are mainly used in computer technology. Computers use binary because they can only read and store an on or off charge, in Binary system 1 represents “on” and 0 represents “off”. Also binary numbers are required by all computer language and programming for discrete information using digital encoding. These discreet bits consist of the zeroes and ones of the binary system.

Decimal Numbers: These are the most widely used format in the number system. Decimal numbers are used in all domains as they are simple readable number consisting of number from 0-9.

Hexadecimal Numbers: Hexadecimal Numbers are used to bridge the gap between computers using binary and humans understanding intelligent Numbers. It is more user friendly.
Do you want me to write out 1110001011101010110001101101001011010110110001101110000000000000000000000

00000000000000000000000000000000000000000000000000000000000000 like that? I find e2eac6d2d6c6e00000000000000000000 much easier to spell for quickconvertor, and far less likely to evoke an error in writing or copying and more information can be shared with lesser characters. One more use of Hexadecimal values are also used in sharing information across nodes in Telecom to maintain a standard between various bodies.

Octal Numbers: Before usage of hexadecimal, octal numbers are widely used in computer world. Octal numbers are divisible by 3 hence they are easy to read by both machine and humans.

TBCD Numbers: Telephony  Binary Coded Decimals are widely used in telecom industry. Hexadecimal numbers are encoded by swapping their octets. TBCD numbers are in octet form i.e constists of 16 binary digits.

In place units number system has bases.

  • Binary Numbers : base 2 (digits 1 and 0 only)
  • Decimal Numbers : base 10 (digits from 0-9)
  • Hexadecimal Numbers : base 16 (digits 0-9 and A-F)
  • Octal Numbers : base 8 (digits 0-7F)


For Eaxmple:

Example 1:Convert string “QC” into Hexadecimal


Hexadecimal value of “Q” is 51 and Hexadecimal value of “C” is 43.

Hexadecimal value for “QC” will be (5143)16

Example 2:Convert string “QC” into Binary


Binary value of “Q” is 01010001 and Binary value of “C” is 01000011.

Binary value for “QC” will be (01010001 01000011)2

Example 3:Convert Binary (01010001 01000011)2 to Decimal


The decimal number is equal to the sum of powers of 2 of the binary number.

0*215+1*214+0*213+1*212+0*211+0*210+0*29+1*28+0*27+1*26+0*25+0*24+0*23+0*22+1*21+1*20= (20803)8

Conversion Table: ASCII Table