We must routinely consider trade$-$offs in computer architecture to realize the full potential of resources

available to us while maximizing the performance of the application or program. Given this, consider that

we want to design a new application$-$specific floating format that uses $8$ bits in memory for each number.

Our main goal is to minimize the memory requirements of the number storage while maximizing the range

of numbers we can represent. The following information is available from the application designers:

The binary representation of the numbers in the application will have at most four bits in the fraction.

That is$,$ the fractional part of the number can range from $`0000\text{'}$ to $\text{'}1111\text{'}.$ With the implied $1,$ the

numbers range from $1\mathrm{.}1111\text{'}.$

The numbers in the application will include exponents as well.

A$)$ Given this information about the application, how many bits would you assign for the sign, exponent,

and fraction to ensure that the possible range of numbers is maximized. Once you assign the number of

bits to the sign, exponent, and fraction, calculate the bias for the new floating$-$point format you just

designed. Please fill in the blanks below. Enter an integer for each question.

B$)$ Represent the decimal number $-1\mathrm{.}1875$ using the new floating point representation from part $($a$).$

Enter the binary representation using $8$ bits here: