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.