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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 .
A common example is the Data General Nova, which was a 16-bit design that performed 16-bit math as a series of four 4-bit operations. 4-bits was the word size of a widely available single-chip ALU and thus allowed for inexpensive implementation. Using the definition being applied to the 68000, the Nova would be a 4-bit computer, or 4/16.
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]
Typical binary register widths for unsigned integers include: 4-bit: maximum representable value 2 4 − 1 = 15; 8-bit: maximum representable value 2 8 − 1 = 255; 16-bit: maximum representable value 2 16 − 1 = 65,535; 32-bit: maximum representable value 2 32 − 1 = 4,294,967,295 (the most common width for personal computers as of 2005),
A minifloat in 1 byte (8 bit) with 1 sign bit, 4 exponent bits and 3 significand bits (in short, a 1.4.3 minifloat) is demonstrated here. The exponent bias is defined as 7 to center the values around 1 to match other IEEE 754 floats [ 3 ] [ 4 ] so (for most values) the actual multiplier for exponent x is 2 x −7 .
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 bits. Conversely, it is the "first" or smallest positive integer that ...
Computing – Computational limit of a 64-bit CPU: 9,223,372,036,854,775,807 (about 9.22 × 10 18) is equal to 2 63 −1, and as such is the largest number which can fit into a signed (two's complement) 64-bit integer on a computer. Mathematics – NCAA basketball tournament: There are 9,223,372,036,854,775,808 (2 63) possible ways to enter the ...
(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 ...