2's Complement

Several options exist for the representation of signed integer values as binary numbers:

1's Complement: A negative number is represented by changing all zeroes to ones and all ones to zeroes. Example for an 8 bit representation of 1 and -1:

Binary Signed Unsigned

0000 0001 1 1

1111 1110 -1 254

Supported Range: -127 to 127. Disadvantage: We have two representations for 0: 0000 0000 and 1111 1111.

2's Complement: Similar to 1's complement but adding 1 for negative numbers:

Binary Signed Unsigned

0000 0001 1 1

1111 1111 -1 255

0111 1111 127 127

1000 0001 -127 129

1000 0000 -128 128

Supported Range: -128 to 127. Disadvantage: There is no corresponding positive number to the smallest negative integer value.

Java, the JVM, and all modern processor architectures use 2's complement.