Floating Point Representation
Course Content Specification
Describe and exemplify floating-point representation of positive and negative real numbers, using the terms mantissa and exponent.
Describe the relationship between the number of bits assigned to the mantissa/exponent, and the range and precision of floating-point numbers.
At present we have used binary to represent integers (whole numbers). But there is a problem at present we cannot store real numbers (numbers with decimal portions). It is also cumbersome to store large integers.
We are accustomed to using a fixed notation where the decimal point is fixed and we know that any numbers to the right of the decimal point are the decimal portion and to the left is the integer part.
E.g. 10.75Â
10 is the Integer Portion and 0.75 is the decimal portion. To get around this problem the computer uses Floating Point Representation.
The number above demonstrates the location of the mantissa and exponent
Mantissa
The mantissa from the example above is 25
Exponent
The exponent from the example above is 5
The computer only stores the Mantissa and the Exponent. It does not need to store the base as it already knows that this will always be 2.
Lesson Video
1.1 Binary lesson 1.mp4