MSP$430$FR$6989$ has instructions to add, subtract, and perform arithmetic bit$-$shifting, but no instructions to divide or multiply. Using this MCU you want to find the average value of the set of decimal numbers $\{2,-47,13,11\}.$ Assume $8-$bit registers and twos complement notation for signed numbers.

First devise a scheme of how you can find the average of these numbers using $8-$bit signed numbers and the given operations $($pairwise addition, subtraction, and bitshifting$).$ Then answer following questions:

$($a$)$ What is the result in bits as it is stored in an $8-$bit register? Enter a binary number. $11111010($b$)$ What is the corresponding value? Enter a decimal number. $-5\mathrm{.}25$

Hint: There are two ways to solve this problem: like a dumb MCU $($adding$/$shifting bit by bit$)$ or like a smart human $($understanding the limits of $8-$bit binary arithmetic and when they apply $-$ they do not apply in all cases$).$