Karnaugh Map
The “Karnaugh map” is a graphical method which provides a systematic method for simplifying and manipulating the Boolean expressions or to convert a truth table to its corresponding logic circuit in a simple, orderly process.
In this technique, the information contained in a truth table or available in SOP or POS form is represented on a K-map.
Although this technique may be used for any number of variables, it is generally used up to 6 variables, beyond which it becomes very cumbersome.
In n-variable K-map there are 2n cells.
“Gray code” has been used for the identification of cells.
Three-variable K-map
- Four cells
- Four minterms (maxterms)
Three-variable K-map
- Eight cells
- Eight minterms (maxterms)
Four-variable K-map
- Sixteen cells
- Sixteen minterms (maxterms)
Implicant
Implicant is a product/sum term in sum of product (SOP) for which the function output must be 1 or sum/maxterm term in product of sum (POS) of a boolean function.
Prime Implicant
A prime Implicant is a smallest possible sum/product term of the given function, removing any one of the literal from which is not possible. All possible groups formed in K-map are prime implicants.
Example: Number of prime implicants = 3
Essential Prime Implicant (EPI)
- Essential Prime Implicant are those prime implicants which cover atleast one minterm in SOP or atleast one maxterm in POS that can’t be covered by any other prime implicant.
- Essential Prime Implicants (EPI) are those prime implicants which always appear in final solution.
Example: Number of Essential Prime Implicants (EPI) = 2.
Redundant Prime Implicants (RPI)
- The prime implicants for which each of its minterm/maxterm is covered by some essential prime implicants are redundant prime implicants (RPI).
- Redundant Prime Implicants (RPI) never appears in final solution.
Example: Redundant Prime Implicant (RPI) = BC
Selective Prime Implicants (SPI)
The prime implicants which are neither essential nor redundant prime implicants are called selective prime implicants. These are also known as non-essential prime implicants.
They may or may not appear in final solution.
Example: Number of selective prime implicants = 2.
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Must Read: What is Boolean algebra?
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