Floating Point Arithmetic

Floating Point arithmetic is an arithmetic operation on floating point numbers which include addition, subtraction, multiplication and division. The operations are done with algorithms similar to those used on sign magnitude integers.

Addition :

Using a 4 digit decimal example;

9.988 x10¹ + 2.332 x 10^-1

>9.988 x 10¹ + 0.023 x 10¹

>9.988 x10¹ + 0.023 x 10¹ = 10.011 x 10¹

>10.011 x 10¹  (overflow) = 1.0011 x 10²

Answer = 1.001 x 10²

Subtraction

Example 2: (subtraction)

Using 4 digit Binary example:

>1.000_­2­ x 2^-1  -1.00­0­₂­ x2^-2 ( 0.5 – 0.25)

>1.000­_2­ x2^-1  - 0.10­0₂ ­x 2_­­­^-1­­

>1.000­_2­ x2^-1  - 0.100­₂ ­x 2_­­­^-1­­ = 0.100­₂ x2^-1

>0.10­0₂ ­x 2_­­­^-1  ( under flow)

Answer = 1.000­_{2 ­}x 2

Multiplication

Using 4bit decimal example:

1.111 x 10¹⁰  X  9.500 x 10^-7

>New exponent = 10 -7 = 3

>1.111 x 9.500 = 10.5545 x 10³

>10.5545 x 10³ (overflow) = 1.056 x 10⁴

Example in binary:

1011.01 x 110.1

           1011.01

          X  110.1

            101101

                    0

       101101

     101101

-------------------
   1001001.001

 ­

Division

11111100 / 110=  101010

                     101010

                  --------------

          110) 11111100

                   110

                   ------------

                      111

                      110

                   -------------     

                          110

                          110

                   -------------

                                 0

                                 0   

                             ------

Rounding

Rounding Decimal:

Example 1:

0.8842       round to 3 decimal places = 0.884

                   round to 2 decimal places = 0.88

round toward + infinity

example 2:

1.23            round to 2 decimal places = 1.3

-2.86          round to 2 decimal places = -2.8

round toward – infinity

example 3

1.23            round to 2 decimal places = 1.2

-2.86          round to 2 decimal places = -2.9