Convert hex to decimal
Please provide values below to convert hexadecimal to decimal, or vice versa.
Definition: The hexadecimal numeral system is a base-16 positional numeral system that uses the same symbols as the decimal system to represent the values of zero to nine (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the letters A, B, C, D, E, and F to represent the values of ten to fifteen. Being a positional numeral system means that each position represents a different magnitude. For example, using the hex number AAA:
AAA = 10 × 162 + 10 × 161 + 10 × 160 = 2560 + 160 + 10 = 2730
As can be seen, although the symbols occupying the three positions shown are the same, "A," the magnitude of each is one power of 16 apart.
History/origin: The term hexadecimal is derived from the prefix "hexa" from Greek for "six" and "decimal," which is derived from the Latin meaning "tenth." The symbols A-F were not always used for the values 10 through 15 in the earlier instances of the hexadecimal system. In the 1950s, some used the digits 0 through 5 with a bar over each value, while others used the letters u through z. Yet others used K, S, N, J, F, and L or even F, G, J, K, Q, and W.
As can be seen, there were many different ways in which the values of 10 through 15 were represented in the past, showing the fairly arbitrary nature of symbol choice. Both capital A-F as well as lower case a-f are used today to represent these symbols.
Current use: The hexadecimal numeral system is widely used throughout computer system design and programming. This is partly due to it being easier for humans to read hexadecimal values than it is for them to read binary-coded values.
Definition: The decimal numeral system is a base-10 numeral system, also known as the Arabic number system, and is the standard system used to represent integer and non-integer numbers, using the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is a system that uses positional notation, where the same symbol is used in different positions, and the magnitude is determined by which "place" the symbol holds. For example, the number 111:
111 = 1 × 102 + 1 × 101 + 1 × 100 = 100 + 10 + 1 = 111
As can be seen, even though each symbol (the "1") is the same in each position, they all have different magnitudes. Decimal fractions can also be represented by using a decimal point (".").
History/origin: Numerals based on ten have been used by many cultures since ancient times including the Indus Valley Civilization, ancient Egyptians, the Bronze Age cultures of Greece, the classical Greeks, and the Romans, among others. Some believe that this is linked to the human hand usually having ten digits.
The positional decimal system in use today has roots as early as around the year 500, in Hindu mathematics during the Gupta period. The earliest known evidence of the Hindu-Arabic numerals being used in Europe was found in the Codex Vigilanus, a compilation of historical documents written in the year 976. The numerals that people today are accustomed to were a result of early typesetting in the late 15th to earthly 16th century.
Current use: The decimal numeral system is the most common system used around the world for the symbolic representation of numbers. It is used ubiquitously for everyday applications, mathematics, and within many other contexts.