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For example, 32 contiguous bits may be treated as an array of 32 Booleans, a 4-byte string, an unsigned 32-bit integer or an IEEE single precision floating point value. Because the stored bits are never changed, the programmer must know low level details such as representation format, byte order, and alignment needs, to meaningfully cast.
The design of floating-point format allows various optimisations, resulting from the easy generation of a base-2 logarithm approximation from an integer view of the raw bit pattern. Integer arithmetic and bit-shifting can yield an approximation to reciprocal square root (fast inverse square root), commonly required in computer graphics.
The resulting 'raw' exponent is a 8 bit binary integer where the leading bits are not '11', thus values 0 ... 1011 1111 b = 0 ... 191 d, appr. bias is to be subtracted. The significand's leading decimal digit forms from the (0)cde or 100e bits as binary integer. The subsequent digits are encoded in the 10 bit 'declet' fields 'tttttttttt ...
CDC 60-bit computers did not have full 60-bit adders, so integer arithmetic was limited to 48 bits of precision from the floating-point unit. Exception processing from divide-by-zero was different on different computers. Moving data between systems and even repeating the same calculations on different systems was often difficult.
For instance, using a 32-bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit. The fractional bits continue the pattern set by the integer bits. The next bit is the half's bit, then the quarter's bit, then the ⅛'s bit, and so on. For example:
The format of an n-bit posit is given a label of "posit" followed by the decimal digits of n (e.g., the 16-bit posit format is "posit16") and consists of four sequential fields: sign: 1 bit, representing an unsigned integer s; regime: at least 2 bits and up to (n − 1), representing an unsigned integer r as described below
If an IEEE 754 quadruple-precision number is converted to a decimal string with at least 36 significant digits, and then converted back to quadruple-precision representation, the final result must match the original number. [3] The format is written with an implicit lead bit with value 1 unless the exponent is stored with all zeros (used to ...
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 networks .