Numerical Precision

1a. Storage of Floating Point Number in the Memory

The numbers which contain decimal points are called floating point numbers. Computer accommodates the number 1.0 as 0.1111111…. means all the bits treated as 1. We could confirm the most extreme number of digits a coasting floating point number less than 1.0 can have. This will give us a thought of the amount of important digits a coasting decimal point number can have. We recognize the biggest binary number less than 1.0 the PC can accommodate - it is 0.1111111..., i.e., all the bits are 1, and confirm how this binary number interprets to decimal one. We might anticipate that this binary number will make as the biggest decimal number less than 1.0, i.e., 0.9999999. We will see that the amount of 9's we get relies on the amount of bits the workstation can accommodate in a memory location.

1b. Discussion about the Ease or Difficulty of Manipulating and Using Floating Point Numbers in Arithmetic Calculations

The easiness and difficulties in floating point numbers vary from arithmetic operations. For instance the multiplication and division operation are easy in floating point numbers while the operation of addition is difficult because to add two floating point values we have to adjust the one that's closer to zero so that they both have the same exponent. Furthermore the subtraction is easy to perform in floating point. (Goldberg, D, 1991)

Opinion about the Memory Efficiency of the Floating Point Format

Among the two formats that are BCD and floating point format now a days the floating point format is more efficient than BCD. The floating point format covers the numeric needs to a larger extent as compared to BCD format. BCD format covers the need of particular formats. It is mentioned above that the floating point numbers occupy less space in memory now we discuss that how BCD occupies the space in memory. The values of BCD are in the form of nibbles while each nibble represents the range 0-15. The single decimal digit is represented by each nibble in BCD. It is therefore with a single byte once can place the values having two digits or the values which range 0-99.

Fig 1

The above figure shows the data representation of BCD in memory and in which it can be seen that it does not represent the efficiency of memory. The BCD format is not only memory inefficient it is ...