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65535 occurs frequently in the field of computing because it is (one less than 2 to the 16th power), which is the highest number that can be represented by an unsigned 16-bit binary number. [1] Some computer programming environments may have predefined constant values representing 65535, with names like MAX_UNSIGNED_SHORT .
The 16-bit word length thus became more common in the 1960s, especially on minicomputer systems. Early 16-bit computers (c. 1965–70) include the IBM 1130, [3] the HP 2100, [4] the Data General Nova, [5] and the DEC PDP-11. [6] Early 16-bit microprocessors, often modeled on one of the mini platforms, began to appear in the 1970s.
The advantage over 8-bit or 16-bit integers is that the increased dynamic range allows for more detail to be preserved in highlights and shadows for images, and avoids gamma correction. The advantage over 32-bit single-precision floating point is that it requires half the storage and bandwidth (at the expense of precision and range). [5]
When the bit numbering starts at zero for the least significant bit (LSb) the numbering scheme is called LSb 0. [1] This bit numbering method has the advantage that for any unsigned number the value of the number can be calculated by using exponentiation with the bit number and a base of 2. [2] The value of an unsigned binary integer is therefore
Bfloat16 is designed to maintain the number range from the 32-bit IEEE 754 single-precision floating-point format (binary32), while reducing the precision from 24 bits to 8 bits. This means that the precision is between two and three decimal digits, and bfloat16 can represent finite values up to about 3.4 × 10 38 .
(With 16-bit unsigned saturation, adding any positive amount to 65535 would yield 65535.) Some processors can generate an exception if an arithmetic result exceeds the available precision. Where necessary, the exception can be caught and recovered from—for instance, the operation could be restarted in software using arbitrary-precision ...
The number of bits needed for the precision and range desired must be chosen to store the fractional and integer parts of a number. 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.
65536 is a superperfect number – a number such that σ(σ(n)) = 2n. [1] A 16-bit number can distinguish 65536 different possibilities. For example, unsigned binary notation exhausts all possible 16-bit codes in uniquely identifying the numbers 0 to 65535. In this scheme, 65536 is the least natural number that can not be represented with 16 ...