$1.$ Consider a hypothetical very$-$less$-$than$-$single precision number format that

uses $1$ bit for the sign, $3$ bits for a biased exponent, and $4$ bits for the fractional

portion of the mantissa. The bias for the exponent is $4.$ Assume exponents of

$000$ and $111$ are reserved.

a$.$ In base $10($i$.$e$.,$ decimal$),$ what is the smallest, positive number that can be

encoded in this format?

b$.$ In base $10,$ what is the largest, positive number that can be encoded in this

format?

c$.$ In base $10,$ what is the second largest, positive number that can be

represented by this format?

d$.$ What do you notice about the step size between $0$ and the smallest positive

number that can be represented by this format comparted to the step size

between the two largest positive numbers?