The Karnaugh map (also known as a Veitch diagram) was invented in 1953 by Maurice Karnaugh, a telecommunications engineer at Bell Labs. It is a graphical way of minimizing Boolean expressions. An expressionâ€™s truth table is drawn as a matrix in such a way that each row and each column of the matrix puts minterms that differ in the value of a single variable adjacent to each other. Then, by grouping adjacent cells of the matrix, you can identify product terms that eliminate all complemented literals, resulting in a minimized version of the expression.
In a Karnaugh map with n variables, a Boolean term mentioning k of them will have a corresponding rectangle of area 2 n âˆ’ k . Common sized maps are of 2 variables which is a 2x2 map; 3 variables which is a 2x4 map; and 4 variables which is a 4x4 map
For problems involving more than six variables, solving the Boolean expressions is more preferred than the Karnaugh map.
A Karnaugh map can also be drawn for 0â€™s as well as 1â€™s
The SOP (Sum of Product) expression refers to drawing of a Karnaugh map in which high values (1â€™s) are plotted. The simplified equation comes in SOP form such as (A.B)+(B.C)
The POS (Product of Sum) expression represents the low (0) values in the Karnaugh Map. The simplified equation comes in POS form like (A+B).(C+D)
Pairs, Quads & Octets
A group of two adjacent 1â€™s in the Veitch Diagram is known as Pair.
The quad is a group of four 1â€™s that are end to end, or in the form of a square. Two variables and their compliments drop out of the Boolean equation in the quad.
An octet is a group of eight adjacent 1â€™s. an octet always eliminates three variables and their complements
Karnaugh maps also allow easy minimizations of functions whose truth tables include " don't care " conditions
They are usually indicated on the map with a hyphen / dash / X in place of the number .
The value can be a " 0, " " 1, " or the hyphen / dash / X depending on if one can use the " 0 " or " 1 " to simplify the Karnaugh Map more .
Be the first to comment