$8.$ Consider the given Mealy machine accepting binary input.

Recall that in a Mealy machine, inputs are not accepted or

rejected but create output. An output always takes place

during transition of states. Suppose input is binary where

the most significant bit $($left$-$most$)$ is the sign $(0$ for $+$ and $1$

for $).$ So $7=100111$ as a $6-$bit number $($int$6\_$t if there

was such a thing$)$ and $7=1111$ as a signed $4-$bit

number $($int$4\_$t$).$ Since binary numbers have their least significant bit on the right$-$most position,

assume that input and output is right$-$to$-$left. For example, $13=01101$ would be fed as $10110$

$($reverse$)$ and $7=100111$ would be fed as $111001($left$-$to$-$right$).$ For each of the following binary

numbers,

i$.$ Determine its value as a signed integer.

ii$.$ Reverse the bits from right$-$to$-$left to left$-$to$-$right, so they can be fed into the machine.

iii. Create the output from the given Mealy machine.

iv$.$ Determine the value of the output by converting back to a signed integer $($reversing$).$

b$.100111$

c$.1111$

d$.000111$

e$.001111$