Operations on integers

1. Addition and subtraction

Operand	Overflow
	Addition	Subtraction
+ve , -ve	no	no
+ve , +ve	If result sign is 1	If result sign is 0
-ve , -ve	If result sign is 0	If result sign is 1

Example:  5 + 4

+5 :  0000 0000 … 0000 0101

+4 :  0000 0000 … 0000 0100

+9 :  0000 0000 … 0000 1001

           

Thus, when adding two positive operand with sign result sign is 1 = overflow.

Example:  5 + (-4)

+5 :  0000 0000 … 0000 0101

-4  :  1111 1111… 1111 1100

+1 :  0000 0000 … 0000 0001

Thus, when adding a positive and a negative  operand = not overflow.

Example:  5 – (+4)

+5 :  0000 0000 … 0000 0101

+4 :  0000 0000 … 0000 0100

+1 :  0000 0000 … 0000 0001

           

Thus, when subtracting two positive operand with sign result sign is 0 = overflow.

2. Dealing with overflow

      I.        Some languages (e.g., C) ignore overflow

·         Use MIPS addu, addui, subu instructions

    II.        Other languages (e.g., Ada, Fortran) require raising an exception

·         Use MIPS add, addi, sub instructions

·         On overflow, invoke exception handler

-       Save PC in exception program counter (EPC) register

-       Jump to predefined handler address

-        mfc0 (move from system control) instruction can retrieve EPC value,

           to return after corrective action

3.Arithmetic for Multimedia

       I.        Graphics and media processing operates on vectors of 8-bit and 16-bit data

·         Use 64-bit adder, with partitioned carry chain

·         Operate on 8×8-bit, 4×16-bit, or 2×32-bit vectors

·         SIMD (single-instruction, multiple-data)

-           

     II.        Saturating operations

·         On overflow, result is largest representable value

-       c.f. 2s-complement modulo arithmetic

·         E.g., clipping in audio, saturation in vide

4. Multiplication and division

# Multiplication

Binary multiplication is just a bunch of right shifts and adds

# Division

Division is just a bunch of quotient digit guesses and left shifts and subtracts dividend = quotient x divisor + remainder

Published by : 

Hafizah binti Ismail  B031310266