Karnaugh Mapping

A Karnaugh map is nothing more than a special form of truth table, useful for reducing logic functions into minimal Boolean expressions.

Here is a truth table for a specific four-input logic circuit:

Complete the following Karnaugh map, according to the values found in the above truth table:

Here is a truth table for a four-input logic circuit:

If we translate this truth table into a Karnaugh map, we obtain the following result:

Note how the only 1’s in the map are clustered together in a group of four:

If you look at the input variables (A, B, C, and D), you should notice that only two of them actually change within this cluster of four 1’s. The other two variables hold the same value for each of these conditions where the output is a “1”. Identify which variables change, and which stay the same, for this cluster.

Here is a truth table for a four-input logic circuit:

If we translate this truth table into a Karnaugh map, we obtain the following result:

Note how the only 1’s in the map all exist on the same row:

If you look at the input variables (A, B, C, and D), you should notice that only two of them are constant for each of the “1” conditions on the Karnaugh map. Identify these variables, and remember them.

Now, write an SOP (Sum-of-Products) expression for the truth table, and use Boolean algebra to reduce that raw expression to its simplest form. What do you notice about the simplified SOP expression, in relation to the common variables noted on the Karnaugh map?