aw the diagram for a finite state machine that detects whether or not a received message is valid. Characters$/$bytes $($of which we can receive any possible value$)$ are received one at a time and valid messages begin with the character $\text{'}$T$\text{'}$ followed by the character $\text{'}$S$\text{'}$ and end with the character $\text{'}$T$\text{'}$ followed by the character $\text{'}$E$\text{'}.$ Since messages can contain any and all possible values they can, of course, contain $\text{'}$T$\text{'}$ bytes. All such $\text{'}$T$\text{'}$s within a message will be received as two $(2)$ consecutive $\text{'}$T$\text{'}$ bytes $($thus differentiating themselves from $\text{'}$TS$\text{'}$ and $\text{'}$TE$\text{'}).$ So$,$ if you receive two $\text{'}$T$\text{'}$ characters that indicates a single $\text{'}$T$\text{'}$ in the actual message.

Your machine will ignore bytes until a $\text{'}$T$\text{'}$ followed by an $\text{'}$S$\text{'}$ is received. Upon receiving the $\text{'}$S$\text{'}$ it will initialize a sum to zero $(0).$ Now your machine must look for a $\text{'}$T$\text{'},$ taking all other bytes and adding them to the sum $($we$\text{'}$re computing a simple checksum$).$ On receiving a $\text{'}$T$\text{'},$ one of the following occurs $($hint: these are separate transitions$)$:

If the next byte is another $\text{'}$T$\text{'},$ add $\text{'}$T$\text{'}$ to the sum and continue to receive bytes,

If the next byte is an $\text{'}$E$\text{'}$ and the sum is zero $(0),$ indicate a valid message,

If the next byte is an $\text{'}$E$\text{'}$ and the sum is not zero $(0),$ indicate a corrupt message, or

If the next byte is not an $\text{'}$E$\text{'}$ and is not a $\text{'}$T$\text{'},$ indicate a corrupt message.

For cases $2,3,$ and $4,$ return to waiting for the start of a new message.

This finite state machine has an initial state but no terminating states. Outputs$/$actions should be included on transitions. As an example, the label S$|$sum$=0$ would indicate that the machine is transitioning on input $\text{'}$S$\text{'}$ and the action is to set the sum to zero. If there is no action to be performed $($e$.$g$.$ the sum is not being changed$/$set$),$ use the action None. Finally, note that your states do not require labels and not including a sum value test as part of a transition's input label implies "don't care" $($or$,$ more accurately, all values of sum$).$ Both of these exceptions simply allow for your diagram to be less cluttered.