A machine stores floating point numbers in $7-$bit words. Employ first bit for the sign

of the number, second one for the sign of the exponent, next two for the magnitude of

the exponent, and the last three for the magnitude of the mantissa.

a$)$ By magnitude, what are the smallest negative and positive numbers in the

system?

b$)$ By magnitude, what are the largest negative and positive numbers in the

system?

c$)$ What is the machine epsilon?

d$)$ Represent $e^1$ in the $7-$bit format.

e$)$ Represent $3\mathrm{.}623$ in the $7-$bit format.