$(15$ pts$)$ Given a $12-$bit floating point number represented in

the following format: $1$ sign bit, $4$ exponent bits, $7$ fraction bits

$($assuming default bias$)$

a$.$ How do you represent $12\mathrm{.}12$ in the above format?

b$.$ What decimal number does the following floating$-$

point number represent:

$001101100010?$

c$.$ What is the smallest normalized number one can

represent in this format?

d$.$ What is the smallest positive normalized number

one can represent in this format?

e$.$ What is the smallest positive non$-$zero de$-$normalized

number one can represent in this format?