Computer Number Systems: An Introduction to Binary, Decimal, and Hexadecimal
The ASCII (American Standard Code for Information Interchange) is a standard organization whose set benchmarks and values are globally accepted. The main reason for accepting an international standard is to prevent the inconvenience caused by each party creating their own numeric system. Thus, the standards set by ASCII are used in production worldwide.
ASCII stands for American Standard Code for Information Interchange. It is a character encoding standard for electronic communication that was first published in 1963. ASCII was created to create a single source of truth for communication among computers in the 20th century.
ASCII’s creation came out of the use of telegraph machines. Computers had a number of different ways to create characters on their systems prior to the 1960s. As computer networking grew, it became clear that there needed to be a consistent way to represent the different characters so that communication could happen between machines.
ASCII codes are used to represent text in computers and telecom devices. ASCII codes are 7-bit long and can encode 128 different characters, including upper- and lowercase letters, numerals, punctuation marks, and some control codes.
The number system is primarily divided into four standard notations according to the ASCII, which are accepted worldwide and used according to convenience in today’s modern machines.
The four standard notations are:
- Binary (either 0 or 1)
- Decimal (digits from 0–9)
- Octal (digits from 0–7)
- Hexadecimal (digits from 0–9 and A-F)
- Numbers following 0–9 in the hexadecimal system are denoted using letters from A to F.
I) Binary:
A binary number is any number expressed in the base 2 system, which uses a mathematical notation of representing numbers using zeros and ones.
Binary is used in a wide range of computer applications. It is an important part of digital devices including computers, smartphones, cameras etc. All of the digital device's process and store information in binary. Binary is furthermore extended to Cryptography where a series of 0’s and 1’s is used to keep them secure. There are unique combinations of these 1 and 0’s created for each and every unique identification.
II) Decimal:
A decimal number is any number expressed in the base 10 system, which is the number system used in our daily lives, and is based on the fact that there are ten digits from 0 to 9.
The Decimal number system is the generic number system you and I use in everyday life. It is used in general arithmetic operations i.e., addition, subtraction, multiplication and division. It is used as a standard representation for measurements and data
III) Octal
An octal number is any number expressed in the base 8 system, which uses digits from 0 to 7 to represent numbers.
Octal is used in computing and mostly in Unix based systems. Unix based systems are Linux Operating systems. Octal is used in representations of file permissions, memory addresses etc. It is used in digital signal processing.
IV) Hexadecimal
A hexadecimal number is any number expressed in the base 16 system, which uses digits from 0 to 9 and letters from A to F to represent numbers. The letters A to F represent numbers from 10 to 15, respectively.
The hexadecimal notation is widely used in computer systems, particularly in programming and digital electronics, as it is a compact way to represent large numbers. For example, the color of a pixel on a computer screen is often represented as a hexadecimal value, which can be easily converted to binary and then used by the computer to display the correct color.
