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The problem is similar in nature to the year 2000 problem, the difference being the Year 2000 problem had to do with base 10 numbers, whereas the Year 2038 problem involves base 2 numbers. Analogous storage constraints will be reached in 2106 , where systems storing Unix time as an unsigned (rather than signed) 32-bit integer will overflow on 7 ...
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
Programs that process years as 16-bit values may encounter problems dealing with either the year 32,768 or 65,536, depending on whether the value is treated as a signed or unsigned integer. For the year 32,768 problem, years after 32,767 may be interpreted as negative numbers, [5] [87] beginning with −32,768 which may be displayed as 32,768 BC.
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]
The overflow flag is thus set when the most significant bit (here considered the sign bit) is changed by adding two numbers with the same sign (or subtracting two numbers with opposite signs). Overflow cannot occur when the sign of two addition operands are different (or the sign of two subtraction operands are the same). [1]
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 range of integer values that can be stored in 16 bits depends on the integer representation used. With the two most common representations, the range is 0 through 65,535 (2 16 − 1) for representation as an binary number, and −32,768 (−1 × 2 15) through 32,767 (2 15 − 1) for representation as two's complement.
Arbitrary-precision arithmetic can also be used to avoid overflow, which is an inherent limitation of fixed-precision arithmetic. Similar to an automobile's odometer display which may change from 99999 to 00000, a fixed-precision integer may exhibit wraparound if numbers grow too