Minimisation using Boolean algebra is not always straight forward and sometimes it is not obvious if a further manipulation would give a simpler circuit.

Karnaugh maps are a much easier method for minimising expressions.

K-maps are a special type of Venn diagram.

K-maps are subdivided into squares and each square represents one minterm.

2 variable K-maps

2-variable K-maps have 4 squares - each representing one of four possible minterms. e.g. for inputs A and B;

One variable is always in inverted or non-inverted form for each row or column.  Not Aidentifies the left hand column and A the right.Not B identifies the top row and B the bottom row.

Any horizontal or vertical movement between adjacent squares on the K-map MUST result in a change of only one variable in the associated minterms.  The following is NOT a K-map.