Test: K Maps - GATE MCQ

A Karnaugh map (K-map) is an abstract form of Venn diagram organized as a matrix of squares, where each square represents a Maxterm or a Minterm.

The given expression A +A’ = 1 is based on non-impact unifying theorem.

Essential prime implicants are prime implicants that cover an output of the function that no combination of other prime implicants is able to cover.

Each group of adjacent Minterms (group size in powers of twos) corresponds to a possible product term of the given function.

It should be kept in mind that don’t care terms should be used along with the terms that are present in minterms as well as maxterms which reduces the complexity of the boolean expression.

There are many situations in logic design in which simplification of logic expression is possible in terms of XOR and XNOR operations.
Expression of XOR : AB’ + A’B
Expression of XNOR : AB + A’B’

In case of XOR/XNOR simplification we have to look for the following diagonal and offset adjacencies. XOR gives output 1 when odd number of 1s are present in input while XNOR gives output 1 when even number of 1s or all 0s are present in input.

In a minterm, each variable w, x or y appears once either as the variable itself or as the inverse. So, the given expression satisfies the property of Sum of Minterm.

Product-of-Sums expressions can be implemented using 2-level OR-AND & NOR logic circuits.

Don’t care conditions can be used for simplifying Boolean expressions in K-maps which helps in pairing with 1/0.