Two's Complement Calculator

What Is Two's Complement?

Two's complement is the standard way computers represent signed integers in binary. The most significant bit (MSB) acts as the sign bit: 0 means positive, 1 means negative.

How to Convert Decimal to Two's Complement

Choose a bit width (8, 16, 32, or 64 bits).
For positive numbers, write the binary and pad with leading zeros.
For negative numbers, invert all bits of the absolute value and add 1.

Example: -37 in 8-bit Two's Complement

37 in binary is 100101. Invert to 011010, add 1 to get 11011011. So -37 is represented as 11011011 in 8-bit two's complement.

Frequently Asked Questions

What is the range of 8-bit signed integers?

8-bit two's complement covers -128 to 127. The positive range is one less than the negative range because zero uses the positive representation.

Why is two's complement preferred over sign-magnitude?

Two's complement lets CPUs use the same addition circuitry for signed and unsigned math. Sign-magnitude also has two representations of zero (+0 and -0).

How do I decode a negative binary number?

If the MSB is 1, invert all bits, add 1, and apply a negative sign to the result. This calculator performs that conversion automatically.

What happens if my number is out of range?

Each bit width has fixed limits. For example, 8-bit signed integers cannot represent 200 or -200. Increase the bit width or use a smaller value.

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What Is Two's Complement?

How to Convert Decimal to Two's Complement

Example: -37 in 8-bit Two's Complement

Frequently Asked Questions

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