Numeral Systems

Binary Decimal Hexadecimal Octal bin dec hex oct converter calculator

Binary to Decimal Decimal to Binary Hex to Decimal Decimal to Hex Octal from Octal Converter from Binary

A numeral system (or system of numeration) is a writing system for expressing numbers. There are many systems used now or that have been used in the past like Roman, Babylonian, Egyptian, Mayan etc. Luckily for us there is one numeral system that is extremely popular and is known by anyone in every country - the decimal system.

Even though there is one universal used by many there are still reasons for us to learn more then one. For example the Binary, the Octal and the Hexadecimal systems are used in any modern computer. Every Coder, Programmer or a Developer should learn them and be able to understend them. Here is a quick summary of the four and after you have read about them you can try our converter to see in practice how they are represented and how they vary by different values.

Binary system

The Binary numeral system is a positional notation with a base of 2. It uses only two digits 0 and 1. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices.

The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifically inspired by the Chinese I Ching.

Octal system

The octal numeral system, or oct for short, is the base-8 number system. It uses the digits from 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation 112.

In the past some Native Americans have used octal systems because they counted using the spaces between their fingers rather than the fingers themselves.

Decimal system

The Decimal numeral system is the most commonly used and the most familiar one to the general public. It is also known as Base 10 numbering system since it is based on those 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In this system, every digit has its own position as well as the decimal point. With the decimal point we can represent fractions. For example 107.5 or 3.14. Some countries use "," as a decimal point and others use "."

Many numeral systems of ancient civilisations use ten and its powers for representing numbers, probably because there are ten fingers on two hands and people started counting by using their fingers.Very large numbers were difficult to represent in these old numeral systems, and, only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. The Decimal numeral system is based and is the extension to the Hindu–Arabic numeral system.

Hexadecimal system

Hexadecimal (also base 16, or hex) is a positional numeral system with a base of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A–F (or alternatively a–f) (the first 6 letters of the English alphabet) to represent values ten to fifteen. Hexadecimal numerals are widely used by computer system designers and programmers, as they provide a more human-friendly representation of binary-coded values. Each hexadecimal digit represents four binary digits, also known as a nibble, which is half a byte. For example, a single byte can have values ranging from 0000 0000 to 1111 1111 in binary form, which can be more conveniently represented as 00 to FF in hexadecimal.

The use of the letters A through F to represent the digits above 9 was not universal in the early history of computers. There are also no signs that numeral systems of base 16 were used in the past.

To convert between Binary, Octal, Decimal and Hexadecimal click here

Read more about Numeral system at Wikipedia