Problem $5$

Suppose a new standard MAE$384-12$ is defined to store floating point numbers using $12$ bits. The first bit is used to store the sign as in IEEE$-754,$ the next $6$ bits store the exponent plus the appropriate bias, and the remaining $5$ bits store the mantissa. As in IEEE$-754,$ an exponent and mantissa of all zero bits is used to indicate true zero, and an exponent of all one bits together with a mantissa of all zero bits is used to store $+/-$ infinity. Determine by hand in decimal format

a$)$ the bias for storing exponents in MAE$384-12$;

b$)$ the smallest possible non$-$zero positive number;

c$)$ the largest possible finite positive number;

d$)$ the smallest possible difference between $1\mathrm{.}010$ and the next larger possible number.

e$)$ the smallest possible difference between $7\mathrm{.}010$ and the next larger possible number.

Problem $5$ required submission:

Handwritten $($or printed$)$ all steps to obtain the answers, incl. the final answers.