Part $4-$ Problem $4(10$ points$)$

Build a "binary odd number detector" MEALY machine that works as follows:

It will read in strings that are in the language $\{0,1\}\{0,1{\}}^{**}\{$#$\}$ over the alphabet $\{1,0,$#$\}.$

You may assume that all strings it processes will be in the language defined above.

Each time it processes a $0$ or a $1$ the machine will print a D $($for digit$)$

When it sees the final pound sign $($#$)$ it should print either T $($for True, if the most recent digit was $1,$ so the number is odd$)$ or F $($for False, if the most recent digit was $0,$ so the number is not odd$).$

$\backslash$table$[[$Examples$],[$Input$,$Result$],[0$#$,$DF$],[1$#$,$DT$],[011$#$,$DDDT$],[10001$#$,$DDDDDT$],[000$#$,$DDDF$]]$

$\backslash$table$[[$More Examples$],[$Input$,$Result$],[111$#$,$DDDT$],[00011$#$,$DDDDDT$],[101010101$#$,$DDDDDDDDDT$],[01010$#$,$DDDDDF$],[111011$#$,$DDDDDDT$]]$

Draw a MEALY machine with at most $8$ states that works as described above.

Note that IT IS possible to draw this machine with fewer than $8$ states, but the most you can use is $8.$

Put your answer to problem $4$ in this box. Make sure you build a MEALY machine and you have no more than $8$ states!!

Scratch area $-$ I WILL NOT GRADE anything written in this box