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 syslem?

b$)$ By magninide, what are the largest negative and positive numbers in the system'?

c$)$ What is the machine epsilon?

d$)$ Represent $e^l$ in the $7-$hit format.

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

f$)$ What is the next higher number, $x_2$ after $x_1=0110110$ in the $7-$bit format.

g$)$ Find $|\frac{x_2,x_1}{x_1}|$ from part $($f$)$ and compare with the machine epsilon.