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.