# Simplify boolean expression using karnaugh map

The algorithm we will study later is tedious for humans but is easy to program using any high-level programming language. Simplify boolean expression using karnaugh map do this find the largest adjacent groups of 1's. Prime Implicant - Implicant that can not be combined with another one to remove a literal. There is no algorithm you can follow that is guaranteed to lead to the simplest cheapest online stock and option trading australia of the expression Given any intermediate result there is no way to tell if it is in fact the simplest form of the expression In this lecture you will learn an algorithmic procedure for finding the simplest two level form of a Boolean expression.

Finally, we circle groups of 1's so that all 1's are circled. An essential prime implicant is a prime implicant that includes a 1 not covered by any other prime implicants. The second example above shows that it works for multiple variable subsets--as long as they are powers of two.

Don't cares act like joker in a deck of playing cards--we can make them whatever we want. Also notice that entries at the ends of the K-map differ by only one element with entries on the other side of the K-map. For small examples it is easy. Write down the minimized expression. Since the function is given in terms of minterms we write the minterm number inside the box that represents simplify boolean expression using karnaugh map minterm.

A K-map shows the value of a function for every combination of input values just like a truth table, but a K-map spatially arranges the values so it is easy to simplify boolean expression using karnaugh map common terms that can be factored out. For example, in the 3 variable K-map above the square with a 2 in it represents the minterm A'BC' and the square with a 6 in it represents the minterm ABC'. For small examples it is easy. You can draw the K-map from a truth table, Boolean expression, etc. Propagational delay determines the speed of the circuit.

For larger expressions with 3 and more variables it because much harder. Note, that with the example above if you're not careful you could end up with an expression with too many prime implicants. Groups must be "square" and the number of 1's in a group must be a power of 2.