Design a circuit that will tell whether a given month has 31 days in it. The month is specified by a 4-bit input, A3:0. For example, if the inputs are 0001, the month is January, and if the inputs are 1100, the month is December. The circuit output, Y, should be HIGH only when the month specified by the inputs has 31 days in it. However, if the input is not a valid month (such as 0 or 13) then the output is don’t care (can be either 0 or 1).

  see attachments

Explanation:

A Karnaugh map for the output is shown in the first attachment. The labeled and shaded squares represent the cases where Y = HIGH. The associated logic can be simplified to

  Y = A3 xor A0

when the don't care at 1110 gives an output of HIGH.

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The second attachment shows a logic diagram using a 4:1 multiplexer to do the decoding. A simple XOR gate would serve as well. If AND-OR-INV logic is required, that would be ...

  Y = Or(And(A3, Inv(A0)), And(A0, Inv(A3)))

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