Two's complement examples

• To convert from two's complement to decimal:
  • Look at leftmost bit to see if it is positive or negative.

  • If positive, convert number from binary to decimal

  • If negative, determine magnitude by:
    • Complement the bits
    • Add 1
    Decimal number is negative of this number

• Example:

  11111111 00001001
  This is a negative number.
  Complement is 00000000 11110110
  Add 1, result is 00000000 11110111 = 247
  So original number was -247.
  

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• To convert from decimal to two's complement:

  • If number is positive, convert number from decimal to binary

  • If number is negative:
    • Convert absolute value of number from decimal to binary
    • Complement the bits
    • Add 1

• Example:

  -8
  Representation of |-8| is 00000000 00001000
  Complement is 11111111 11110111
  Add 1, result is 11111111 11111000 (in hex: fff8 - see table p. 218)