Floating-Point Representation

• Very large numbers cannot be represented using fixed-point notation, nor can very small fractions.
• For decimal numbers, we get around this limitation by using scientific notation.

Example:
976000000000 can be represented as 9.76 × 10¹¹.
0.00000000000976 can be represented as 9.76 × 10^–12.

• This same approach can be taken with binary numbers. We can represent a number in the form M × B^±E
  where, M is mantissa, E is exponent

• In order to simply operations, floating point numbers are normalized. A normalized number is one in which the most significant digit of mantissa is 1. Thus, a normalized non zero number is on in the form ± 1.bbb …. b × 2^±E.

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