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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.
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
In the case of an integer, the variable definition is restricted to whole numbers only, and the range will cover every number within its range (including the maximum and minimum). For example, the range of a signed 16-bit integer variable is all the integers from −32,768 to +32,767.
For the next range, from 2 53 to 2 54, everything is multiplied by 2, so the representable numbers are the even ones, etc. Conversely, for the previous range from 2 51 to 2 52, the spacing is 0.5, etc. The spacing as a fraction of the numbers in the range from 2 n to 2 n+1 is 2 n−52.
The width, precision, or bitness [3] of an integral type is the number of bits in its representation. An integral type with n bits can encode 2 n numbers; for example an unsigned type typically represents the non-negative values 0 through 2 n − 1.
Swift introduced half-precision floating point numbers in Swift 5.3 with the Float16 type. [20] OpenCL also supports half-precision floating point numbers with the half datatype on IEEE 754-2008 half-precision storage format. [21] As of 2024, Rust is currently working on adding a new f16 type for IEEE half-precision 16-bit floats. [22]
A 32-bit register can store 2 32 different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. With the two most common representations, the range is 0 through 4,294,967,295 (2 32 − 1) for representation as an binary number, and −2,147,483,648 (−2 31) through 2,147,483,647 (2 31 − 1) for representation as two's complement.
The exponent range for normal numbers is [−126, 127] for single precision, [−1022, 1023] for double, or [−16382, 16383] for quad. Normal numbers exclude subnormal values, zeros, infinities, and NaNs. In the IEEE binary interchange formats the leading 1 bit of a normalized significand is not actually stored in the computer datum.