The months of the years are coded in four variables, STUV, such that January is

Question

The months of the years are coded in four variables, STUV, such that January is 1011, February is 1010.... and December is 0000. The remaining four combinations are never used. (Remember 30 days has September, April June and November, all the rest has 31, except February Create the truth table for a function, "M", that is 1 if the month has 31 days and 0 if it does not Implement the truth table for problem, 11, using two 3 out of 8 decoders shown (the function table is provided). Clearly show the how the inputs, STUV are connected to the decoders inputs and enables ("G" inputs) and the decoder outputs are connected to implement the function "M"

Explanation / Answer

Answer:

Truth table of function: There are 12 months in a year. We will represent each month as per the serial number of their occurrence in the year. It means that January will be represented by 1, February by 2, March by 3 and so on. In the last, December will be 12. In binary, these numbers can be represented by 4 bit binary numbers. So, the truth table for the said function will be:

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Karnough map:

Month Days Number S T U V Y January 31 11 1 0 1 1 1 February 28/29 10 1 0 1 0 0 March 31 9 1 0 0 1 1 April 30 8 1 0 0 0 0 May 31 7 0 1 1 1 1 June 30 6 0 1 1 0 0 July 31 5 0 1 0 1 1 August 31 4 0 1 0 0 1 September 30 3 0 0 1 1 0 October 31 2 0 0 1 0 1 November 30 1 0 0 0 1 0 December 31 0 0 0 0 0 1

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