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Numerical Conversions

A numeral system (or system of numeration) is a writing system for expressing numerals, and a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner. It can be seen as the context that allows the numeral "11" to be interpreted as the binary numeral for three, the decimal numeral for eleven, or other numbers in different bases.

In arithmetic, the radix or base refers to the number b in an expression of the form bn. The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n".

The most commonly used system of numerals is known as Hindu-Arabic numerals. The Arabic numerals are the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). They are descended from Indian numerals and the Hindu-Arabic numeral system developed by Indian mathematicians, by which a sequence of digits such as "406" is read as a whole number. The Arabic numerals are encoded in ASCII (and Unicode) at positions 48 to 57.

The base-10 system (decimal) is the one most commonly used today. Egyptians, beginning in 2,000 BCE, exactly wrote rational numbers into Egyptian fraction base 10 numbers. It is assumed to have originated because humans have ten fingers.

The binary numeral system, or base-2 number system represents numeric values using two symbols, usually 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right).

In mathematics and computer science, hexadecimal (also base-16, hexa, or hex) is a numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or a through f) to represent values ten to fifteen.

Below is a Javascript Numerical Converter between the Decimal, Binary, Octal and Hexademical systems:

Numerical Converter
Decimal:
Binary:
Octal:
Hexademical: