$[20]$ Question $1$: Express the following numbers in $10-$bit floating point format. In this representation $5$ bits are reserved for mantissa and $4$ bits are reserved for the exponent and $1$ bit is reserved for the sign of the number. For the exponent take bias $\backslash (=7\backslash )[5]$ d$)$ How big can the number $\backslash ($ c $\backslash )$ be such that the result of the following calculation is numerically $0$ in this $10-$bit floating point format $?\backslash [8+$c$-8=0\backslash ][20]$ Q$2$: Consider the following function

$f(x)=sin(x)$

$[5]$ a$)$ Expand the function at the expansion point $x_0=0$ using $1^{st}$ order Taylor series. Quantify

the accuracy of this approximation by evaluating the approximation at the following $x$ values.

What is the order of accuracy of this approximation?

$[5]$ b$)$ Expand the function at the expansion point $x_0=\frac{}{2}$ using $1^{st}$ order Taylor series. Quantify

the accuracy of this approximation by evaluating the approximation at the following $x$ values.

What is the order of accuracy of this approximation?

$[10]$ c$)$ Plot $f(x)=sin(x)$ and its first order Taylor Series expanded at the expansion point $x_0=\frac{}{2}$

in Matlab in the same figure.