# Simplify boolean expression using karnaugh map

Don't cares act like joker in a deck of playing cards--we can make them whatever we want. For example, if you choose A'B first you would then have to choose A'C' and BC to cover every implicant in the on-set. Next we put a 1 in each square where the function has the value 1. Prime Implicant - Implicant that can not be combined with another one to remove a literal. 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 simplify boolean expression using karnaugh map find common terms that can be factored out.

Note, that with the example above if you're not careful you could end up with an expression with too many prime implicants. Since the function is given in simplify boolean expression using karnaugh map of minterms we write the minterm number inside the box that represents that minterm. This observation is the motivation for the formal K-map procedure that follows. Essential Prime Implicant - A prime imlpicant that includes a minterm not covered by any other prime implicant. Find the essential prime implicants.

Since the function is given in terms of minterms we write the minterm number inside the box that represents that minterm. Note, that with the example above if you're not careful you simplify boolean expression using karnaugh map end up with an expression with too many prime implicants. You already know one method for simplifying Boolean expressions: Later we will study an algorithmic method that works for functions of any number of variables.

Two Level Form of a Boolean Expression The two level form of an expression refers simplify boolean expression using karnaugh map the number of subexpressions in the Boolean equation or the number of gates in the longest path through the gate implementation of the expression. Prime Implicant - Implicant that can not be combined with another one to remove a literal. Find the prime implicants. For example, if you choose A'B first you would then have to choose A'C' and BC to cover every implicant in the on-set. Note, that with the example above if you're not careful you could end up with an expression with too many prime implicants.

The second example above shows that it works for multiple variable subsets--as long as they are powers of two. The karnaugh, or k-map, method is fast and best carried out by a human. A K-map shows the value of a function for every combination of input values just like a truth table, but simplify boolean expression using karnaugh map K-map spatially arranges the values so it is easy to find common terms that can be factored out. What follows is a more formal description of how to proceed. If there are any 1's not covered by prime implicants, carefully select prime implicants to cover the remaining 1's.

What follows is a more formal description of how to proceed. Note, you may have to try several selections to find the minimal form of the expression. We circle only groups that are powers of 2 and try to create circles as large as possible. This numbering guarantees that adjacent terms differ by only one term. Find the essential prime implicants.

Since this is a function of 3 variables we first draw the outline for a 3-variable K-map. Simplify boolean expression using karnaugh map two examples above make it look easy to remove subexpressions with Boolean algebra. Two Level Form of a Boolean Expression The two level form of an expression refers to the number of subexpressions in the Boolean equation or the number of gates in the longest path through the gate implementation of the expression.

The algorithm we will study later is tedious simplify boolean expression using karnaugh map humans but is easy to program using any high-level programming language. This numbering guarantees that adjacent terms differ by only one term. If both of these terms appear as minterms in an expression we could factor out the A: What follows is a more formal description of how to proceed.