The working hours of a factory are 8 hours a day, divided into three shifts: from 8 to 11 (first shift), from 11 to 13 (second shift), from 13 to 16 (rest) and from 16 to 19 (third shift). It is intended to design a circuit that has as inputs the binary representation of the current hour minus eight and that provides the output of the shift number that is working (if applicable) or "0" if it is break time. It is requested: - Express the minimal output and implementation functions as a sum of products and as a product of sums. - Obtain the expressions corresponding to each of the previous functions carried out with a single type of doors.

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