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In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system 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 ...
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:
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural ...
Octal ( base 8) is a numeral system with eight as the base . In the decimal system, each place is a power of ten. For example: In the octal system, each place is a power of eight. For example: By performing the calculation above in the familiar decimal system, we see why 112 in octal is equal to in decimal.
Conversion of the fractional part: Consider 0.375, the fractional part of 12.375. To convert it into a binary fraction, multiply the fraction by 2, take the integer part and repeat with the new fraction by 2 until a fraction of zero is found or until the precision limit is reached which is 23 fraction digits for IEEE 754 binary32 format.
This is because the radix of the hexadecimal system (16) is a power of the radix of the binary system (2). More specifically, 16 = 2 4, so it takes four digits of binary to represent one digit of hexadecimal, as shown in the adjacent table. To convert a hexadecimal number into its binary equivalent, simply substitute the corresponding binary ...
Double-precision binary floating-point is a commonly used format on PCs, due to its wider range over single-precision floating point, in spite of its performance and bandwidth cost. It is commonly known simply as double. The IEEE 754 standard specifies a binary64 as having: Sign bit: 1 bit. Exponent: 11 bits.
Usage. Use: {{Hexadecimal|x}} where x is the decimal number to be converted to a hexadecimal. Decimals and fractions will be rounded down. The number is, by default, formatted with a final subscript 16 to display the base. An optional second parameter of |hex will replace the base with "hex". To opt out of the subscript, use a second parameter ...