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Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
Consider encoding the value −118.625 as an HFP single-precision floating-point value. The value is negative, so the sign bit is 1. The value 118.625 10 in binary is 1110110.101 2. This value is normalized by moving the radix point left four bits (one hexadecimal digit) at a time until the leftmost digit is zero, yielding 0.01110110101 2.
That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hexadecimal "10" is the same as a decimal "16" and a hexadecimal "20" is the same as a decimal "32".
Thus only 23 fraction bits of the significand appear in the memory format, but the total precision is 24 bits (equivalent to log 10 (2 24) ≈ 7.225 decimal digits) for normal values; subnormals have gracefully degrading precision down to 1 bit for the smallest non-zero value. The bits are laid out as follows:
Base36 is a binary-to-text encoding scheme that represents binary data in an ASCII string format by translating it into a radix-36 representation. The choice of 36 is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z (the ISO basic Latin alphabet). Each base36 digit needs less than 6 ...
The C99 and C11 standards of the C language family, in their annex F ("IEC 60559 floating-point arithmetic"), recommend such an extended format to be provided as "long double". [18] A format satisfying the minimal requirements (64-bit significand precision, 15-bit exponent, thus fitting on 80 bits) is provided by the x86 architecture.
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A numeric character reference uses the format &#nnnn; or &#xhhhh; where nnnn is the code point in decimal form, and hhhh is the code point in hexadecimal form. The x must be lowercase in XML documents. The nnnn or hhhh may be any number of digits and may include leading zeros. The hhhh may mix uppercase and lowercase, though uppercase is the ...