Define The Karnaugh Maps (K Maps)

The Karnaugh map (K map) provides the systematic method for simplifying a Boolean expression or a truth table function when used properly the K map will produce the simplest SOP or POS expression possible. Acquaintance with the law and rules of Boolean algebra is not required. As an alternative, simplification is done graphically using the K mapping technique.

The K map is the table consisting of N = 2ⁿ cells, where n is the number of input variables. For the SOP expression each cell represents one particular combination of the variables in product form. A table format is such that there is a single variable change between any adjacent cells and this is the characteristic the will determine adjacency. To exemplify the above points let us consider an example where n = 2 and N = 4. Assuming the input variable are A and B then the K map illustrating the four (4) possible variable combinations A ¯B, ¯AB, A ¯B and AB is show below is show below

Two variable K map format

If we extend our illustration to consider the case where n = 3 and N = 8 then assuming that our input variables are A, B and C the associated K Map.

The Three Variable K-Map