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In IEEE 754 parlance, there are 10 bits of significand, but there are 11 bits of significand precision (log 10 (2 11) ≈ 3.311 decimal digits, or 4 digits ± slightly less than 5 units in the last place).
Each of these number systems is a positional system, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hexadecimal weights are powers of 16. To convert from hexadecimal or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. For example:
Intel hexadecimal object file format, Intel hex format or Intellec Hex is a file format that conveys binary information in ASCII text form, [10] making it possible to store on non-binary media such as paper tape, punch cards, etc., to display on text terminals or be printed on line-oriented printers. [11]
Hexadecimal can easily be mapped to bytes because two hexadecimal digits is a byte. Base32 does not map to individual bytes. However, two Base32 digits correspond to ten bits, which can encode (32 × 32 =) 1,024 values, with obvious applications for orders of magnitude of multiple-byte units in terms of powers of 1,024.
However, on modern standard computers (i.e., implementing IEEE 754), one may safely assume that the endianness is the same for floating-point numbers as for integers, making the conversion straightforward regardless of data type. Small embedded systems using special floating-point formats may be another matter, however.
Hexspeak is a novelty form of variant English spelling using the hexadecimal digits. Created by programmers as memorable magic numbers, hexspeak words can serve as a clear and unique identifier with which to mark memory or data. Hexadecimal notation represents numbers using the 16 digits 0123456789ABCDEF.
The standard recommends providing conversions to and from external hexadecimal-significand character sequences, based on C99's hexadecimal floating point literals. Such a literal consists of an optional sign ( + or - ), the indicator "0x", a hexadecimal number with or without a period, an exponent indicator "p", and a decimal exponent with ...
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.