How do you describe a boolean function using a K-Map in such a way that the boolean function depends on the previous value of this function?
How to implement a K-Map with negative feedback
boolean-algebradigital-logickarnaugh map
Related Solutions
To construct the truth table, you need to manually assess each combination. A table works well, hence the name "truth table"! I assume you understand logical ANDs and ORs, to make sense of this answer.
First, you want to solve each ANDed group separately. Boolean algebra has the same order of precedence as standard algebra, with AND treated like multiplication, and OR treated like addition. Put these answers in a table. Don't worry, I'll attach a picture to demonstrate. Once you have all of these statements figured out, then you can OR them together. Follow the red lines on the following table:
Now that the table is completed, you can build a map. One of the standard configurations is shown below. You have two bits defining the columns, and the other two bits defining the rows. Find the square that intersects the binary inputs (A, B, C, and D), and fill in the answer from your truth table. I've done two of them, in Purple and Orange:
I'll leave the rest for you! You didn't ask how to solve the K-Map. I assume you know how?
Take care!
(P.S. I've included a typo in the truth table. Can you find it?)
How well a karnaugh map can simplify is downto the creator of the map with regards to drawing optimal loops.
How to determine whether what has been drawn (post further boolean reduction) is not really possible with k-maps on their own
One option is the use of Espresso Heuristic Logic reduction via a fantastic piece of software called: Logic friday ( http://www.sontrak.com/ ) Quite often this has reduced some logic of mine even further as I usually forget the odd one or two don't care states
The real question however is ... is this check on reduction for personal/professional use (in which case carry on) or homework? because if it is homework and logicFriday realises a further simplification, you had better be able to realise it via k-maps for the marks
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Best Answer
If the present output depends on previous output, then use the previous output as as one of the variable in truth table and K-map.
Take JK flipflop as an example: