Two’s Complement Calculator

This two’s complement calculator converts a signed whole number into the exact binary pattern a computer would store it in, using the scheme almost every processor relies on for negative integers. Enter any whole number, positive or negative, then choose a bit width of 8, 16 or 32 bits to match the size you are working with. The calculator returns three results: the two’s complement binary pattern padded to the full width, the equivalent hexadecimal value, and the unsigned decimal value that the same bit pattern represents if read without a sign. Two’s complement works by storing negative numbers as two to the power of the bit width plus the value, which makes the leftmost bit act as a sign bit, 1 for negative and 0 for zero or positive, and lets processors add and subtract without special-case logic for negative numbers. If your number falls outside the range the chosen width can hold, for example beyond minus 128 to 127 at 8 bits, the calculator flags it as out of range rather than showing a wrong answer, so you know to pick a wider width. It suits students learning binary arithmetic, programmers debugging low-level code, and anyone checking how a negative value looks in memory. Try the built-in example of minus 5 at 8 bits to see the working before entering your own numbers.

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Signed integer

Bit width

11111011

Hexadecimal0xFB

Unsigned value251

The formula

For a width of w bits, a value v is stored as v if it is zero or positive, or as 2^w + v if it is negative. The pattern fits values from minus 2^(w-1) up to 2^(w-1) minus 1. The leading bit is the sign bit.

Worked example

For minus 5 in 8 bits: 2^8 + (minus 5) = 256 minus 5 = 251, which is 11111011 in binary and FB in hex. Enter -5 with 8-bit selected to confirm.

Frequently asked questions

What is two’s complement?

A way to store signed integers in a fixed number of bits, where a negative number n is held as 2 to the width plus n. It makes addition and subtraction uniform.

What range fits in 8 bits?

Minus 128 to 127. In general minus 2 to the (width minus 1) up to 2 to the (width minus 1) minus 1.

What is the sign bit?

The leftmost bit. If it is 1 the number is negative, if 0 it is zero or positive.

Who this calculator is for

This calculator is for students, programmers and anyone exploring number theory.

What this calculator assumes

You enter a signed integer within the range of the chosen width.
The width is 8, 16 or 32 bits.
Results are shown as the stored bit pattern.

Formula and sources

Related calculators

Prime Factorization Calculator: break a number into prime factors.
LCM Calculator: lowest common multiple.
GCF Calculator: greatest common factor.

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