Arithmetics For Computers (Number System & Operations) - Floating Point Representation

Floating Point Representation :  i)  very small numbers

                                                ii) very large numbers

Floating point has it’s own standard :

1         .       Define by IEEE Std.

2         .       Almost adopted globally

3         .       Contain of 2 representation :-

-          Single precisions

-          Double precisions

IEEE floating has it’s own format :

31   30                               23 22                                0

s

Exponent (E)

Fraction (F)

FORMULA is : X=(-1)^s * (1+ Fraction) * 2^{(exponent – bias)}

S can be 2 values 0 or 1

If 0 means is non negative

If 1 means is negative

The exponent  E  is the power 2 must be raised to in the scientific notation of number.

The exponent is biased with value 127 and the range is between “[(-126) – 127]”

For exponent    -  single : 8 bits
                        -  double : 11 bits

For fraction  -  single :  23 bits
                    -  double :  52 bits

Exponent is excess representation , also can be written as “actual exponent+bias”

-          This is to ensure the exponent is unsigned

-          In single : bias = 127

In double : bias = 1203

Normalized significand :-

•          The value is between  1.0 < significand <2.0
•          Always has a leading pre-binary-point 1 bit
•       Significand is FRACTION with “1“ restored.

LIM ZERKIE 
B031210127