Two's Complement

Sign-magnitude, ones' complement and two's complement of an integer in 8, 16 and 32 bits, and two's complement to decimal.

What to find:

sign-magnitude, ones' and two's complement codes of a number

the number from a two's complement code

The leftmost bit is the sign bit: 0 is plus, 1 is minus. Positive numbers look the same in all three codes.

Test yourself

The number codes calculator writes an integer in sign-magnitude, ones' complement and two's complement in 8, 16 or 32 bits and converts a two's complement code back to a number.

Integer codes

The leftmost bit is the sign bit: 0 for positive numbers, 1 for negative. A positive number looks the same in all three codes. For a negative number:

sign-magnitude — a sign bit of 1 and the absolute value in binary;
ones' complement — all bits except the sign bit are inverted;
two's complement — 1 is added to the ones' complement; the same as 2ⁿ − |x|.

Computers store integers in two's complement, so subtraction becomes addition. n bits hold numbers from −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1 (−128 to 127 in 8 bits).

Example. −45 in 8 bits: |−45| = 0101101, sign-magnitude 1010 1101, ones' complement 1101 0010, two's complement 1101 0011.