Floating Points

Numbers with fraction are called real numbers like The alternative notation for the last two numbers is called scientific notation, which has a single digit to the left of the decimal point. Its format is 
   ±d.ffff...×10±eeee...
Floating point describes a system for numerical representation in which a string of digits (or bits) represents a rational number. For example, a fixed-point representation that has seven decimal digits, with the decimal point assumed to be positioned after the fifth digit, can represent the numbers 
   12345.67, 8765.43, 123.00, ...
whereas a floating-point representation with seven decimal digits could in addition represent 
   1.234567, 123456.7, 0.00001234567, 1234567000000000, ...
A number in scientific notation that has no leading 0s is called a normalized number and floating-point numbers should be normalized. Examples of normalized FP numbers include 
   5.341×103  and  -1.101101×2-3
and examples of not normalized FP numbers include 
   0.05341×105  and  -1101.101×2-6
Normalized floating points have many advantages and hardware using them is standardized, therefore simplified.




      I wanted to speak up during the meeting,    
      but I held my peace (be silent).