Question

The task is to design a binary finite state automaton (FSA) to accept all strings that represent valid messages (for the below code given and parity property) and reject all others. The FSA must be deterministic and reduced finite state acceptor in standard form. Codes are as following: A = 00000 B = 0100 C = 011 Parity = Odd 0, the entire message (including the check digit) has an odd number of 1's. FOR EXAMPLE if your codes are A = 101, B = 1101, C = 001 and your parity property is Odd0, the message ABAC would get encoded as 10111011010011. The final character is the check digit. It is a ‘1’ because we want an odd number of 0s. So 10111011010011 is valid, but 10111011010010 and 10111011011100 are not. Make sure you correctly understand this example before you go further. ABAC is 1011101101001. It has 5 0s, so it already has an odd number of 0s. We have to add a check digit to keep this number odd, so the check digit in this case is 1. If the parity property had been Even0 the check digit would have been 0. Thanks alot.

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