K-Maps (Karnaugh Maps) - GATE CSE (CSE) Digital Logic Free MCQ Test

Entries known as diagonal mapping. The diagonal mapping holds true when for any relation, there is a projection of product on the factor.

These logic gates(XOR, XNOR, NOR) are widely used in digital design and therefore are available in IC form as digital circuits deal with data transmission in the form of binary digits.

Using the transformation method we can realize any POS realization of OR-AND with only NOR.

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

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

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.

There are 16 = (2⁴) cells in a 4-variable K-map.

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.

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’

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.