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Number Conversions

Numbers can be represented in different format e.g. binary, decimal, hexadecimal, octal, ASCII. Please find the different conversions below to convert the numbers from one format to the other one.

ASCII Text Conversions

ASCII stands for American Standard Code for Information Interchange, is one of the most common character encoding standards for electronic communication. ASCII is based on 128 characters and includes 26 letters of English language in upper and lowercase formats, numbers from 0 to 9 and various punctuation marks e.g. !%&/" etc. Owing to the fact that computers can only understand numbers, the ASCII code represent text and characters with different numbers and in this way computers understands and display various text. We must be aware of that capital Letter "C" and small letter "c" are two distinct values and ASCII value of 'C' is 43 (decimal) and 01000011 (binary). Similary the ASCII value of 'c' is 63 (decimal) and 01100011 (binary). All the 26 English letters in capital and small are the distinct letters and every letter is assigned a specific ASCII value.

Binary Conversions

The binary numeral system uses the number 2 as it base or radix and it consists of only two numbers 0 and 1. The use of these binary numbers was prevalent since ancient times in medieval Golden Age and scientists like Al-Khwarizmi, Avicenna and Jamshid Al-Kashi made significant advaces in algebra, mathematics, trignometry and geometry. Since then, the usage of binary numeral system has played a vital role in understading modern scientific aspects e.g. detecting electrical signals where "0" represents the "off" state while "1" represents the "on" state. Modern computers are completely based on binary numeral system and all the data is interpreted in binary formats. The numbers can be represented in binary format using the powers to the base 2 i.e. 20, 21 etc.

Decimal Conversions

Decimal numbers uses the number 10 as its base (radix). The decimal numeral system or base-10 numeral system uses 10 symbols (10 decimal digits "0, 1, 2, 3, 4, 5, 6, 7, 8, 9"). Decimal numeral system is the standard system for representing integer and non-integer numbers. Decimal numeral system is basically represented using the powers to the base 10 (100, 101, 102, 10-1 etc.), therefore numbers can be represented to the nth power based on their position. Let's consider a simple example to understand this in detail.

Hexadecimal Conversions

Hexadecimal numbers or hex numbers uses the number 16 as its base (radix). The hexadecimal numeral system or base-16 numeral system uses 16 symbols (10 decimal digits "0, 1, 2, 3, 4, 5, 6, 7, 8, 9" and first six letters of English Language "A, B, C, D, E and F"). These letters are used to represent values from 10 to 15.

Octal Conversions

The octal numeral system uses the number 8 as its base or radix. It uses 8 numbers (0, 1, 2, 3, 4, 5, 6 and 7). Since 8 is equal to 2 raised to the power 3 23, therefore octal system were widely used for the machines that employ word sizes divisible by three e.g. 6-bit, 12-bit, 24-bit and 36-bit. In the modern times, hexadecimal numbers are widely used instead of octal system. To represent one digit of octal number, three bits are required. The maximum digit in the octal numeral system is 7 which can be represented in binary as "111".

by Wasim Khan and it was last modified on