Hexadecimal

Table de correspondance entre le Bibinaire et les autres notations

Bruce Martin hexadecimal notation proposal

Base-16 digits

Hexadecimal-counting

Hewlett-Packard Model HP-16C Programmable RPN Calculator, HP's First and Only Calculator esp. for Programmers, built 1982-1989 (edited to rectangular, V2)

Hexadecimal (also base-16, or hex) is a positional 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"–"F" (or alternatively "a"–"f") 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 00000000 to 11111111 in binary form, which can be more conveniently represented as 00 to FF in hexadecimal.

Usage

In computing, hexadecimal is used extensively for convenience as it is much easier for humans to read than binary code. It is used in programming, for defining colors in HTML and CSS, specifying memory addresses, and in the representation of MAC addresses and IPv6 addresses.

Representation

The standard hexadecimal notation is to prefix the number with "0x" (used in C and languages derived from it), or "$" (used in assembly language), or "0h" (used in Pascal), to denote a hexadecimal number. For example, the decimal number 255 can be written as "0xFF" in hexadecimal.

Conversion

From Hexadecimal to Decimal

To convert a hexadecimal number to decimal, multiply each digit in the hexadecimal number by 16 raised to the power of its position number (counting from 0, from right to left) and sum the results. For example, 1A3 in hexadecimal can be converted to decimal by calculating (1 * 16^2) + (10 * 16^1) + (3 * 16^0) = 419 in decimal.

From Decimal to Hexadecimal

To convert a decimal number to hexadecimal, divide the number by 16 and record the remainder. Continue dividing the quotient by 16 until you get a quotient of zero, recording each remainder. The hexadecimal number is the sequence of remainders read from bottom to top. For example, to convert 419 to hexadecimal, the process would yield the hexadecimal number 1A3.

Mathematics

In mathematics, hexadecimal is one of the simplest ways to express binary numbers in algebra and arithmetic operations. It is also used in certain number theory and cryptography applications where its properties closely relate to those of binary and modular arithmetic.

History

The concept of hexadecimal dates back to the early days of computing as a method of simplifying the representation and manipulation of binary-coded data. Its adoption was driven by the need for efficient computing and the limitations of hardware and software at the time.

See Also

• Binary numeral system
• Octal
• Decimal
• Radix
• Computer science

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