Two's Complement

• Exploits finite size of data representations (cyclic groups) and properties of binary arithmetic.

• To get negative of binary number, invert all bits and add 1 to the result.

  • e.g. 1 = 0 0 0 0 0 0 0 1 in 8-bit
    • invert bits: 1 1 1 1 1 1 1 0
    • add 1: 0 0 0 0 0 0 0 1
    • result: 1 1 1 1 1 1 1 1 = -1

• In 8 bits, signed char ranges from -128 to +127.

Notes: