$4.[4$ pts$]$ Draw a Turing Machine that accepts the set of all bitstrings that have $"0"$ in all the even$-$numbered positions starting with position $0$ at the left. So the $\backslash (\backslash$mathbf$\{$T M$\}\backslash )$ should accept and reject strings such as the following $($I show you all strings of length $\backslash (0-5\backslash )$ bits$).$ The table contains hints to help you $($note bold underlining$).$ You can do this in $4$ states $($maybe fewerl$).$ But more states would be OK$,$ too. Think of the diagrams above, one node is the starting state, one node is the Accept state, and the rest are working nodes.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline String & Result & String & Result & String & Result & String & Result $\backslash \backslash$

$\backslash$hline Empty & reject & $0000$ & Accept & $00000$ & Accept & $10000$ & reject $\backslash \backslash$

$\backslash$hline $0$ & Accept & $0001$ & Accept & $00001$ & reject & $10001$ & reject $\backslash \backslash$

$\backslash$hline $1$ & reject & $0010$ & reject & $00010$ & Accept & $10010$ & reject $\backslash \backslash$

$\backslash$hline $00$ & Accept & $0011$ & reject & $00011$ & reject & $10011$ & reject $\backslash \backslash$

$\backslash$hline $01$ & Accept & $0100$ & Accept & $00100$ & reject & $10100$ & reject $\backslash \backslash$

$\backslash$hline $10$ & reject & $0101$ & Accept & $00101$ & reject & $10101$ & reject $\backslash \backslash$

$\backslash$hline $11$ & reject & $0110$ & reject & $00110$ & reject & $10110$ & reject $\backslash \backslash$

$\backslash$hline $000$ & Accept & $0111$ & reject & $00111$ & reject & $10111$ & reject $\backslash \backslash$

$\backslash$hline $001$ & reject & $1000$ & reject & $01000$ & Accept & $11000$ & reject $\backslash \backslash$

$\backslash$hline $010$ & Accept & $1001$ & reject & $01001$ & reject & $11001$ & reject $\backslash \backslash$

$\backslash$hline $011$ & reject & $1010$ & reject & $01010$ & Accept & $11010$ & reject $\backslash \backslash$

$\backslash$hline $100$ & reject & $1011$ & reject & $01011$ & reject & $11011$ & reject $\backslash \backslash$

$\backslash$hline $101$ & reject & $1100$ & reject & $01100$ & reject & $11100$ & reject $\backslash \backslash$

$\backslash$hline $110$ & reject & $1101$ & reject & $01101$ & reject & $11101$ & reject $\backslash \backslash$

$\backslash$hline $111$ & reject & $1110$ & reject & $01110$ & reject & $11110$ & reject $\backslash \backslash$

$\backslash$hline & & $1111$ & reject & $01111$ & reject & $11111$ & reject $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$*$No copy$/$paste please$*$