karnaugh mapping
Karnaugh Mapping, better known as K-Mapping, is a shortcut that gets around boolean algebra. Variables are split as evenly as possible among the top and side (2 on each in the picture). All variables start at naught, and only one is changed at a time until all possible combinations have been created. The truth table is then used to fill in the cells from its outputs. Any pair, square, or complete row of 1's can be grouped and any variable that changes is removed from the expression and the new simplified condition is outputted.