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The sign bit determines the sign of the number (including when this number is zero, which is signed). The exponent field is an 11-bit unsigned integer from 0 to 2047, in biased form: an exponent value of 1023 represents the actual zero. Exponents range from −1022 to +1023 because exponents of −1023 (all 0s) and +1024 (all 1s) are reserved ...
The number 2,147,483,647 (or hexadecimal 7FFFFFFF 16) is the maximum positive value for a 32-bit signed binary integer in computing. It is therefore the maximum value for variables declared as integers (e.g., as int ) in many programming languages.
Some programming languages such as Lisp, Python, Perl, Haskell, Ruby and Raku use, or have an option to use, arbitrary-precision numbers for all integer arithmetic. Although this reduces performance, it eliminates the possibility of incorrect results (or exceptions) due to simple overflow.
Most of the major Prolog systems support arbitrary precision integer numbers. Python: the built-in int (3.x) / long (2.x) integer type is of arbitrary precision. The Decimal class in the standard library module decimal has
The maximum signed 32 bit value (2 31 − 1) 16,777,216: 0100 0000 The largest consecutive integer in IEEE 754 single precision (2 24) 65,535: FFFF The maximum unsigned 16 bit value (2 16 − 1) 32,767 7FFF The maximum signed 16 bit value (2 15 − 1) 255: FF The maximum unsigned 8 bit value (2 8 − 1) 127 7F The maximum signed 8 bit value (2 ...
Programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information, which may work on (some) 32-bit computers, but fail on 64-bit computers with 64-bit pointers and 32-bit integers. This issue is resolved by C99 in stdint.h in the form of intptr_t.
On 5 January 1975, the 12-bit field that had been used for dates in the TOPS-10 operating system for DEC PDP-10 computers overflowed, in a bug known as "DATE75". The field value was calculated by taking the number of years since 1964, multiplying by 12, adding the number of months since January, multiplying by 31, and adding the number of days since the start of the month; putting 2 12 − 1 ...
Signed 32- and 64-bit integers will only hold at most 6 or 13 base-36 digits, respectively (that many base-36 digits can overflow the 32- and 64-bit integers). For example, the 64-bit signed integer maximum value of "9223372036854775807" is "1Y2P0IJ32E8E7" in base-36. Similarly, the 32-bit signed integer maximum value of "2147483647" is "ZIK0ZJ ...