What is two's complement?

Two's complement is the standard way computers store signed integers. A negative value −n at width w is stored as 2^w − n, so the most significant bit acts as the sign bit and addition works without special cases.

What happens if my number is out of range?

Each width has a fixed signed range (for 8-bit it is −128 to 127). If you enter a value outside the range the tool warns you and shows the wrapped-around encoding.

Is anything sent to a server?

No — the conversion happens entirely in your browser and nothing is uploaded.

How do I find the two's complement of a negative number by hand?

Take the binary of the absolute value, invert every bit, then add 1. The tool does this for you and also shows the equivalent 2^w − n result.

Why does the same bit pattern have two values?

A bit pattern can be read as unsigned (always non-negative) or signed (where the top bit means negative). The tool shows both so you can see how the same bits differ by interpretation.

What are the signed ranges for each width?

8-bit is −128 to 127, 16-bit is −32,768 to 32,767, 32-bit is about ±2.1 billion, and 64-bit is roughly ±9.2 quintillion.

Does it handle 64-bit values accurately?

Yes. The tool uses big-integer arithmetic, so 64-bit conversions are exact rather than losing precision like ordinary floating-point numbers would.

Two's Complement Calculator

Two’s complement calculator

This tool shows how a signed decimal integer is stored in two’s complement form at 8, 16, 32, or 64 bits, with the binary pattern, the hexadecimal value, and both the unsigned and signed readings of the same bits. It is for programmers, students, and anyone debugging low-level numeric encodings.

How it works

Two’s complement is how nearly every modern CPU represents negative integers. For a width of w bits, a negative value −n is stored as 2^w − n, which makes the most significant bit act as a sign bit and lets addition and subtraction share one circuit. The tool masks your value to w bits and then:

binary   = the w-bit pattern of (value mod 2^w)
hex      = that pattern in base 16
unsigned = the pattern read as a non-negative number (0 … 2^w − 1)
signed   = the pattern read in two's complement (−2^(w−1) … 2^(w−1) − 1)

Each width has a fixed signed range; values outside it are flagged and shown wrapped. Big-integer arithmetic keeps even 64-bit results exact.

Example

For −42 at 8 bits: 2^8 − 42 = 256 − 42 = 214, whose 8-bit pattern is 11010110 (hex D6). Read as unsigned that is 214; read as signed two’s complement it is −42.

Width	Signed range
8-bit	−128 … 127
16-bit	−32,768 … 32,767
32-bit	−2,147,483,648 … 2,147,483,647

Everything runs locally in your browser.