Arithmetic for Computers : Integer arithmetics

  • addition

    • start from lsb, carry out values added to next digits
    • overflow: result of the operation is out of range
      • positive + negative -> no overflow
      • positive + positive -> overflow if res is neg
      • negative + negative -> overflow if res is pos

  • subtraction

    • negation of second operand + perform addition
    • overflow: result of the operation is out of range
      • positive - negative -> overlow if neg
      • negative - positive -> overflow if pos
      • positive - positive -> no overflow
      • negative - negative -> no overflow

  • programming languages dealing with overflow

    • addu, addui, subu ignores overflow: treating like unsigned arithmetics, which ignores sign bits
    • invoke exception handler
      • push pc to epc (exception program counter)
      • jump to predefined handler address

  • arithmetic for multimedia

    • 8bit, 16bit used: small data size

  • multiplication

    • long multiplication approach: multiplicand * multiplier bit by bit

  • division

  • overflow