Two\u2019s Complement Calculator

This two\u2019s complement calculator shows how a signed whole number is stored in a fixed number of bits, the scheme almost every computer uses for negative integers. Enter a value and choose 8, 16 or 32 bits, and the calculator returns the two\u2019s complement binary pattern, the hexadecimal form, and the unsigned value that the same bits represent. In two\u2019s complement a negative number is stored as the bit pattern for two to the power of the width, plus the number, so the most significant bit acts as a sign bit and arithmetic just works without special cases. The method, a worked example and the assumptions are set out below.

Signed integer

Bit width

Hexadecimal

Unsigned value

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\u2019s 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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