page_title: Hexadecimal
section_title: Verbal and digital representations
hierarchical_section_title: Hexadecimal / Representation / Verbal and digital representations
caption_attribution_description: How to count hexadecimal from 00 to FF with the 8 fingers and 2 thumbs.
context_page_description: In mathematics and computing, hexadecimal is a positional system that represents numbers using a base of 16. Unlike the common way of representing numbers with ten symbols, it uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values zero to nine, and "A"–"F" to represent values ten to fifteen.
  Hexadecimal numerals are widely used by computer system designers and programmers, as they provide a 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 conveniently represented as 00 to FF in hexadecimal.
  In mathematics, a subscript is typically used to specify the base, also known as the radix. For example, the decimal value 10,995 would be expressed in hexadecimal as 2AF3₁₆. In programming, a number of notations are used to support hexadecimal representation, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, which would denote this value by 0x2AF3.
context_section_description: There are no traditional numerals to represent the quantities from ten to fifteen – letters are used as a substitute – and most European languages lack non-decimal names for the numerals above ten. Even though English has names for several non-decimal powers (pair for the first binary power, score for the first vigesimal power, dozen, gross and great gross for the first three duodecimal powers), no English name describes the hexadecimal powers (decimal 16, 256, 4096, 65536, ... ). Some people read hexadecimal numbers digit by digit like a phone number, or using the NATO phonetic alphabet, the Joint Army/Navy Phonetic Alphabet, or a similar ad hoc system. In the wake of the adoption of hexadecimal among IBM System/360 programmers, Robert A. Magnuson suggested in 1968 in Datamation Magazine a pronunciation guide that gave short names to the letters of hexadecimal - for instance, "A" was pronounced "ann", B "bet", C "chris", etc. Another naming system was invented independently by Tim Babb in 2015. An additional naming system has been published online by S. R. Rogers in 2007 that tries to make the verbal representation distinguishable in any case, even when the actual number does not contain numbers A-F. Examples are listed in the tables below.
  Systems of counting on digits have been devised for both binary and hexadecimal.
  Arthur C. Clarke suggested using each finger as an on/off bit, allowing finger counting from zero to 1023₁₀ on ten fingers. Another system for counting up to FF₁₆ (255₁₀) is illustrated on the right.
caption: Hexadecimal finger-counting scheme
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