Two's Complement (Cambridge (CIE) O Level Computer Science)

Two's Complement

What is two's complement?

• Two's complement is a method of using signed binary values to represent negative numbers

• Using two's complement the left most bit is designated the most significant bit (MSB)

• To represent negative numbers this bit must equal 1, turning the column value in to a negative

• Working with 8 bits, the 128 column becomes -128

• In the example above to represent -1, add column values with a 1 to the MSB

  • MSB (-128)

  • Add 64 (-128+64 = -64

  • Add 32 (-64+32 = -32)

  • Add 16 (-32+16 = -16)

  • Add 8 (-16+8 = -8)

  • Add 4 (-8+4 = -4)

  • Add 2 (-4+2 = -2)

  • Add 1 (-2+1 = -1)

• The two's complement representation of -1 is 11111111

Quick two's complement conversion

• To represent -76

• Write out the positive version of the number

• Starting from the least significant bit (right most column), copy out the binary values up to and including the first 1

• For the remaining digits, invert them (0s to 1s/1s to 0s)

• -128 + 32 + 16 + 4 = -76

• The two's complement representation of -76 is 10110100