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