Question

Concern the following 16-bit floating point representation: The first bit is the sign of the number (0 = +, 1 = -), the next nine bits are the mantissa, the next bit is the sign of the exponent, and the last five bits are the magnitude of the exponent. All numbers are normalized, i.e. the first bit of the mantissa is one, except for zero which is all zeros.

1. How many significant binary digits do numbers in this representation have? How many significant decimal digits does that correspond to?

3. How many different numbers can be represented?

4.What is the largest number? (in both 16-bit binary floating point and explicit decimal representations

5. What is the smallest number? (in both 16-bit binary floating point and explicit decimal representations)

6. What non-zero number is closest to zero? (in both binary and decimal)

Answer 1

Here is the solution. Please do upvote thank you.

1.This representation has 9 bits for mantissa so significant Binary digits are 9 which corresponds to 3.31 or approximately 3 significant decimal digits.

4.The largest number representable is: 65504

Largest number (Binary) : 0 11110 1111111111

5.The smallest number representable is: 0.000061035156

Smallest number (Binary) : 0 00001 0000000000

6.Smallest non zero number : 0.000000059604645

Smallest non zero number (Binary) :

(0 00000 0000000001) base 2 = (0001) base 16