Signed Integer Range Calculator

Most modern computers represent signed integers using two’s-complement notation. In an n-bit signed integer, the highest-order bit participates in the sign and the remaining bit patterns cover both negative and nonnegative values.

Because half of the available bit patterns correspond to negative values, the signed range is not symmetric around zero. There is always one more negative value than positive values.

For an n-bit two’s-complement signed integer, the minimum and maximum values are calculated using:

For example, an 8-bit signed integer uses n = 8. The exponent is therefore 7, giving a minimum of −2⁷ = −128 and a maximum of 2⁷ − 1 = 127.

A 16-bit signed integer contains 65,536 possible bit patterns. Half represent negative values and half represent zero plus positive values.

The 32-bit signed integer remains one of the most commonly encountered integer formats in programming languages, operating systems, file structures, databases, protocols, and APIs.

A signed 64-bit integer provides an extremely large whole-number range and is commonly known as int64, long long, signed long on some systems, or BIGINT in database contexts.

A signed two’s-complement integer has one more negative value than positive values. For example, int8 runs from −128 through +127 rather than −127 through +127.

This happens because zero uses one of the nonnegative bit patterns. With 256 total 8-bit patterns, 128 patterns are interpreted as negative, while the remaining 128 represent zero through 127.

The smallest signed n-bit integer has a binary pattern containing a leading 1 followed entirely by zeros. The largest signed value begins with 0 followed entirely by ones.

A fixed-width integer cannot directly represent a value smaller than its minimum or larger than its maximum. Attempting to store such a value can cause integer overflow, wrapping, trapping, saturation, or another result depending on the programming language, processor, compiler, or runtime.

For example, decimal 128 cannot be represented as an 8-bit signed integer because the maximum int8 value is 127.

Data type selection

Developers can compare expected application values against the limits of int8, int16, int32, int64, or a custom-width integer before selecting a storage type.

Binary protocol analysis

Signed fields in packet formats often specify an exact number of bits. Calculating the valid range helps verify whether decoded values are possible.

Embedded registers

Sensors and hardware registers frequently use nonstandard widths such as 10, 12, 14, 20, or 24 signed bits. A custom range calculator is especially useful in these situations.

Integer widths do not need to be limited to powers of two or common CPU sizes. A packed structure or hardware field may use almost any width.

Using the unsigned formula

The maximum unsigned value is 2^n−1, but the signed maximum is only 2^(n−1)−1.

Expecting a symmetric range

Two’s-complement signed ranges contain one more negative value than positive values.

Ignoring the bit width

The exact same decimal number may fit one integer width and overflow another. Width is therefore essential when discussing integer limits.

Using ordinary JavaScript numbers for very large ranges

JavaScript’s standard Number type cannot exactly represent every large integer. This calculator uses BigInt so wide integer boundaries remain exact.