Interesting Problem 3 : Decimal to Floating Point Conversion

1. Assuming your not restricted to using normalized form, list all the bit patterns that could be used to represent the value 3/8 using the floating- point format described in Figure contains an 8 bit floating point format "a 1 bit sign bit, b. 3 bit exponent, and c. 4 bit mantissa" A= Sign bit, B= Exponent, C=Mantissa. A B B B C C C C. One of the answers is: 01000110,

My solution:

As stated in the question one of the solutions is 01000110.

So assuming this is the first representation of 3/8 in floating –point format.

3/8 can be written as 0.011 in binary having decimal and integer part.

01000110 is 0110.0 × 2^-4

So other solutions will be

01000011 is 0011.0 × 2^-3

01100001

01110000

The last two solutions are not precise due to fewer bits in Mantissa. This is the limitation of floating point numbers. Preciseness can be improve by having representation in more bits .