Two’s Complement Calculator

How it is calculated

Given a whole number n and a width of w bits, the tool first checks that n fits the range −2w−1 ≤ n ≤ 2w−1 − 1. For a negative n it computes n + 2w, which is exactly the invert-and-add-one rule. Positive numbers and zero are written as ordinary binary. The result is padded with leading zeros to exactly w digits. The width must be a whole number from 2 to 32. Anything else gives no result: a fractional number, a width of 1 or 33, or a value outside the range for that width (for example 128 or −129 with 8 bits). The output is a bit string, not a decimal value, and it has no unit.

Common mistakes

• Choosing a width that is too small. With 8 bits the range ends at 127 and −128, so 128 or −129 returns nothing; widen to 16 bits for those.
• Reading the result as an unsigned number. 11010110 is −42 in 8-bit two's complement but 214 if you treat it as unsigned.
• Forgetting the width. The same −1 is 11 in 2 bits, 1111 in 4 bits and 32 ones in 32 bits, so the bit count must match your system.
• Entering a binary or hex string as the number. The box expects an ordinary decimal integer, such as −42.
• Expecting a symmetric range. Two's complement has one more negative value than positive: −128 exists in 8 bits (10000000), but +128 does not.