Q. Explain about Floating Point Representation?

Floating-point number representation includes two parts. The first part of number is a signed fixed-point number which is called mantissa and second part signifies decimal or binary point position and is called an Exponent. Mantissa can be an fraction or simply an integer. Please keep in mind that position of decimal or binary point is presumed and it's not a physical point thus wherever we are representing a point it's only assumed position. 

A decimal + 12.34 in a distinctive floating point notation can be signified in any of subsequent two forms:

This number in any of above forms (if represented in BCD) needs 17 bits for mantissa (1 for sign and 4 every decimal digit as BCD) and 9 bits for exponent (1 for sign and 4 for every decimal digit as BCD). Please note the exponent denotes correct decimal location. In first case where exponent is +2 denotes that actual position of decimal point is two places to right of assumed position whereas exponent- 2 denotes that assumed position of point is two places in the direction of left of assumed position. The assumption of position of point is generally same in a computer resulting in a consistent computational environment. 

Floating-point numbers are frequently represented in normalised forms. A floating point number whose mantissa doesn't comprise zero as most significant digit of number is considered to be in normalised form. For illustration a BCD mantissa + 370 that is 0 0011 0111 0000 is in normalised form since these leading zero's aren't part of a zero digit. On the other hand a binary number 0 01100 isn't in a normalised form. The normalised form of this number is: