Create your answer on engineer's paper following the format in "Homework Sample.pdf$"($Canvas$)$

A thermostat measures air temperature and turns air conditioning on $/$ off at certain thresholds.

$1\mathrm{.}1.$ Is the air temperature analog or digital?

$1\mathrm{.}2.$ Is the output of the thermostat analog or digital?

$1\mathrm{.}3.$ What prevents the thermostat from switching on$/$off rapidly? $($Hint: Look up "Hysteresis".$)$

Convert ${101101\mathrm{.}101}_2$ unsigned to hexadecimal, octal and decimal with full accuracy.

Convert ${14\mathrm{.}57}_8($unsigned$)$ to decimal with accuracy of $4$ digits if rounding is necessary.

Convert ${7654\mathrm{.}7654}_8($unsigned$)$ to hexadecimal.

Calculate $11010110-10110111($unsigned$)$ and express the result in decimal.

Extend the following binary numbers from a $4$ bit wide integer with $4$ bit fraction system into an $8$ bit integer with an $8$ bit fraction so the same value is represented.

First, assume the numbers are signed binary numbers.

a$)0110\mathrm{.}0100$

b$)1010\mathrm{.}0001$

c$)1100\mathrm{.}1$

d$)$ e$)$ f$)$ Now repeat, assuming $a,b,c$ are unsigned numbers.

Convert these decimal numbers first to hexadecimal, then binary, then octal, then back to decimal. As a check $-$ the final answer should agree with the original number.

a$)23\mathrm{.}48$

b$)4\mathrm{.}16$

c$)28\mathrm{.}28$

Convert these decimal numbers first to $6$ bit signed $2\text{'}$s complement binary. Then find the $2\text{'}$s complement of each number. Finally, add the two binary numbers $($pos $/$ neg$)$ together $($should $=0)$

a$)23$

b$)-31$

c$)-17$

Compute the following decimal arithmetic problems in $8$ bit signed binary

a$)93-63$

b$)-31+111$

c$)17-128$

What range of decimal numbers can be expressed in the following number systems?

a$)8$ bit signed $2\text{'}$s complement?

b$)8$ bit unsigned binary

c$)16$ bit signed $2\text{'}$s complement?

d$)16$ bit unsigned binary.