Design a $12-$bit floating point representation of decimal numbers. Use $1$th bit for sign, bits $2-8$

as mantica and bits from $9$ to $12$ for exponent. Do not reserve any bit of exponent for storing

special cases such as $(+0_{,}+0,+,-{)}_{?}.$ Use the bits as afficient as possible.

a$)$ Descirbe a step by strep procedure, given a decimal numer how to store in your $12-$bit

representation.

b$)$ Explain how do you use the exponent bits: range of $($smallest and largest vlaues$)$ exponents

and mantissa.

c$)$ What are the smallest and largest binary and decimal numbers represented?

d$)$ What is machine epsilon as a binary and decimal number?