Floating point representation

The floating point representation of a number has two parts. The first part represents a signed, fixed point number called the mantissa. The second point designates the position of the decimal point and is called as the exponent. The fixed mantissa may be a fraction or an integer.

EX: The decimal number 6132.789 is represented as

     Fraction          Exponent
+ 0.6132789           +04

Floating point representation of a number is shown in the following form m x re
The floating point binary number is presented in similar manner except that it uses base 2 for the exponent.

EX:- The binary number +1001.11 is represented with an 8-bit fraction and 6-bit exponent as follows

Fraction              Exponent
01001110           000100

The floating number equivalent to m x 2e = +(.1001110)2 x 2+4

A floating point number is said to be normalized if the most significant digit of the mantissa is non zero. For example, the decimal number 350 is normalized but 0035 is not. The 8-bit binary number 0011010 is not normalized because of the three leading 0’s.

The number can be normalized by shifting it three positions to the left and discarding the leading 0’s to obtain 11010000. To keep the same value for the floating point number the exponent must be subtracted by 3.

Gray Code:

The reflected binary code is also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit.

The code that exhibits only a single bit change from one code number to the next is known as gray code. In other words gray code number refers from the preceding number by a single bit . As they are no specific weights assigned to the bit position. Hence this code is unweighted code. The advantage of the gray code over binary number is the gray code changes only one bit as it sequence form one number to next

3-bit gray code

Related Topics : Computer Organization & Architecture