Question $1$: $16-$bit floating point format. $(5$marks$)$

The half$-$precision $(16-$bit$)$ floating point is one of the ways to store the numbers

in computer memory. The half$-$precison has the following format,

Sign Bit: $1$ bit

Exponent: $5$ bits

Mantissa: $10$ bits

For all questions, show your work and justify your answers.

a$)$ How many positive numbers can be exactly represented in this floating point

format as normalized floating point values. Express you answer as a formula in

terms of the number of bits in the Matissa and in the Exponent, as well as a final

value. Justify your answer.

$\%$ type your answer here.

b$)$ What is the largest positive number that can be represented using half$-$precision format?

$\%$ type your answer here.

c$)$ What is the smallest positive normalized number that can be written in half$-$

precision format?

$\%$ type your answer here.

d$)$ What is the smallest positive sub$-$normal $($denormalized$)$ number which can be

represented in half$-$precision format?

$\%$ type your answer here.