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In the sign–magnitude representation, also called sign-and-magnitude or signed magnitude, a signed number is represented by the bit pattern corresponding to the sign of the number for the sign bit (often the most significant bit, set to 0 for a positive number and to 1 for a negative number), and the magnitude of the number (or absolute value ...
For signed zoned decimal values, the rightmost (least significant) zone nibble holds the sign digit, which is the same set of values that are used for signed packed decimal numbers (see above). Thus a zoned decimal value encoded as the hex bytes F1 F2 D3 represents the signed decimal value −123: F1 F2 D3 1 2 −3
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:
Thus, Q12 means a signed integer with any number of bits, that is implicitly multiplied by 2 −12. The letter U can be prefixed to the Q to denote an unsigned binary fixed-point format. For example, UQ1.15 describes values represented as unsigned 16-bit integers with an implicit scaling factor of 2 −15 , which range from 0.0 to (2 16 −1)/2 ...
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.
For example, a two's complement signed 16-bit integer can hold the values −32768 to 32767 inclusively, while an unsigned 16 bit integer can hold the values 0 to 65535. For this sign representation method, the leftmost bit ( most significant bit ) denotes whether the value is negative (0 for positive or zero, 1 for negative).
The F16C extension in 2012 allows x86 processors to convert half-precision floats to and from single-precision ... (2 11) ≈ 3.311 decimal ... Hex Value Notes 0 ...
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.