FLOATING POINT REPRESENTATION

Summary

IEEE 754 Floating point is the most common representation used to store real numbers in a computer.

Index

1. What are floating point numbers
2. How to represent a floating point number.
a. Single and Double precisions
3.Data ranges

What are floating point numbers?

The term ‘floating point’ refers to the decimal point (or) binary point in a real number.
The decimal point placed in between group of digits is called floating point numbers.

Ex: 28.36, 0.00124

Floating point number representation IEEE 754 standard:

Floating point number contains three components
1. Sign bit - Represents the sign of floating point number.
2. Exponent - Represents the magnitude of the exponent (explained at later part) (Ex: 1.086 * 10^6)
3. Mantissa - Represents the precision bits of the number. (Ex: 1.086 * 10^6)


Single Precession floating point representation (32bit):


Summary:


31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
S  ------ E-8bit------ -----------------------------M-23bit-------------------

Double Precession floating point representation (64bit):



Sign - 1bit, Exponent 11-bit, Mantissa - 52bit

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