Question $2$:

$($a$)$ Consider the following floating point format: S EE MMM where:

S $=$ sign bit

EE $=$ two bit exponent stored in excess$-2$ notation

MMM $=3$ bit mantissa stored in normalized form.

There is no hidden $`1\text{'}$ bit in the mantisaa and the base is $4.$

$($i$)$ State whether each of the following mantissas is normalized or not:

$001$

$010$

$011$

$100$

$($ii$)$ Give the decimal value of the smallest positive number which can be represented in this format.

$($iii$)$ Express the decimal number $+3\mathrm{.}5$ in this format $.$

$($b$)$ Give the value as a real decimal number the value represented by the IEEE $75432-$bit floating point n

umber $4020000($this is the hexadecimal representation of the IEEE $754$ number$).$