Two's Complement Calculator

Two’s complement defines signed interpretation; it does not by itself define byte order.

Mode

Signed decimal integer

Bit width

—Two's complement uses an explicit signed bit width.

Check the number representation

Keep number base, bit width, signedness and byte order explicit instead of letting one representation silently imply another.

ParseIdentify the input base or prefix before calculation.

RepresentCross-check binary, octal, decimal and hexadecimal views.

CalculateUse arithmetic or bitwise operations with exact integer scope.

Inspect bitsChoose width, signed interpretation, shifts and byte order explicitly.

Copy / verifyCopy only after checking the representation your code or protocol expects.

Base arithmetic Binary calc Hex calc Bitwise Shift Signed/unsigned IEEE-754 Endian

All developer-number calculations run locally. Fixed-width tools model integer bit patterns, not language-specific undefined behavior, CPU flags, binary protocol schemas or floating-point reinterpretation unless a dedicated tool says so.

Range, hex & overflow audit

Expose the signed range for the selected width and verify the same bit pattern as signed, unsigned and hexadecimal.

Bit-width evidence

Hex prefix

Group bits

Overflow policy

Use the tool above, then refresh this audit.

Audit uses the visible inputs plus the assumptions shown here.

Practical guide and verification

Bit width is part of the value

Two’s-complement interpretation depends on a fixed bit width. The same hex or binary pattern can represent a different signed number when interpreted with a different number of bits.

Positive and negative ranges

An n-bit signed two’s-complement integer ranges from −2^(n−1) through 2^(n−1)−1. The asymmetry means the most negative value has no positive counterpart in the same width.

Common mistake

Do not invert bits and add one without first fixing the width. Leading zeros or ones are significant when you are representing a finite-width signed integer.

Bit-pattern resize, sign-extension & overflow audit

Keep the primary decimal/binary conversion, then treat a two’s-complement value as a fixed-width machine bit pattern. Resize it by sign extension, zero extension or truncation and inspect signed/unsigned interpretations, hexadecimal form, discarded bits and round-trip safety.

Bit patternSource widthTarget widthResize operation

—Source signed value

—Source unsigned value

—Result bit pattern

—Result signed value

—Overflow / information loss

Stage	Width	Binary	Hex	Signed	Unsigned

Ready.

Widths are limited to 64 bits and are evaluated with BigInt so the browser does not lose integer precision. Truncation can preserve low-order bits while changing the signed numeric value.

Representation is context

A hexadecimal or binary string does not automatically tell you whether a value is signed, how wide it is, whether bytes are little endian, or whether the bits represent an integer or floating-point value.