$2.($theoretical$,5$ points$)$ Consider a binary floating point number system $$ with $1$ bit for sign,

$7$ bits for mantissa and $5$ bits for exponent. We mimic single precision format and reserve ex$-$

ponents $(00000)2$ and $(11111)2$ for special numbers $(\backslash$pm zeros, $\backslash$pm infinities, subnormal numbers,

etc.$).$ The rest of the exponents $(00001)2<=<=(11110)2$ are used to represent normalized

numbers. We further stipulate that the actual exponent is computed by $(12345)215$

so that there are negative exponents. You are now asked to answer the following questions:

$(1)$ An example of a normalized number $$ in $$ may be: $=1|0011011|10011$ and the value

it represents is $(1)1\backslash$times $(1\mathrm{.}0011011)2\backslash$times $2(10011)215.$ Note that the red bit in front of the

mantissa is not actually stored. It$$s assumed to be there for normalized numbers so