# Question: circuit 1 using a multiplexer a simple but not too...

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Circuit 1 Using a Multiplexer: A simple (but not too secure!) data security system encodes (or converts) from one form to another before storage or transmission. Design a circuit to encode unsigned 4-bit binary numbers. The scheme will add an extra bit, labeled as “X”, added according the following rule. Each number will have 5 bits, the 4 bits of the unsigned binary number plus a parity bit X. The encoding works as follows:

All numbers exactly divisible by 3 (without any remainder) must be transmitted with even parity. (Recall that even parity means that the number of ‘1’ bits in ABCDX is even).

All other numbers must be transmitted with odd parity. (The number of ‘1’ bits in ABCDX is odd).

Create a truth table that has: a row for every input combination and an indication of the corresponding output bit X.

Create a Karnaugh map for bit X.