**Digital Circuits Questions and Answers – Karnaugh Map**

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Karnaugh Map”.

**1. A Karnaugh map (K-map) is an abstract form of ____________ diagram organized as a matrix of squares.**

a) Venn Diagram

b) Cycle Diagram

c) Block diagram

d) Triangular Diagram

**Answer:**a

**Explanation:**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.

**2. There are ______ cells in a 4-variable K-map.**

a) 12

b) 16

c) 18

d) 8

**Answer:**b

**Explanation:**There are 16 = (2

^{4}) cells in a 4-variable K-map.

**3. The K-map based Boolean reduction is based on the following Unifying Theorem: A + A’ = 1.**

a) Impact

b) Non Impact

c) Force

d) Complementarity

**Answer:**b

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

**4. Each product term of a group, w’.x.y’ and w.y, represents the ____________in that group.**

a) Input

b) POS

c) Sum-of-Minterms

d) Sum of Maxterms

**Answer:**c

**Explanation:**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.

**5. The prime implicant which has at least one element that is not present in any other implicant is known as ___________**

a) Essential Prime Implicant

b) Implicant

c) Complement

d) Prime Complement

**Answer:**a

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

**6. Product-of-Sums expressions can be implemented using ___________**

a) 2-level OR-AND logic circuits

b) 2-level NOR logic circuits

c) 2-level XOR logic circuits

d) Both 2-level OR-AND and NOR logic circuits

**Answer:**d

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

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

a) Function

b) Value

c) Set

d) Word

**Answer:**a

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

**8. Don’t care conditions can be used for simplifying Boolean expressions in ___________**

a) Registers

b) Terms

c) K-maps

d) Latches

**Answer:**c

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

**9. It should be kept in mind that don’t care terms should be used along with the terms that are present in ___________**

a) Minterms

b) Expressions

c) K-Map

d) Latches

**Answer:**a

**Explanation:**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.

**10. Using the transformation method you can realize any POS realization of OR-AND with only.**

a) XOR

b) NAND

c) AND

d) NOR

**Answer:**d

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

**11. There are many situations in logic design in which simplification of logic expression is possible in terms of XOR and _________________ operations.**

a) X-NOR

b) XOR

c) NOR

d) NAND

**Answer:**a

**Explanation:**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’

**12. These logic gates are widely used in _______________ design and therefore are available in IC form.**

a) Sampling

b) Digital

c) Analog

d) Systems

**Answer:**b

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

**13. In case of XOR/XNOR simplification we have to look for the following _______________**

a) Diagonal Adjacencies

b) Offset Adjacencies

c) Straight Adjacencies

d) Both diagonal and offset adjencies

**Answer:**d

**Explanation:**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.

**14. Entries known as _______________ mapping.**

a) Diagonal

b) Straight

c) K

d) Boolean

**Answer:** a

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

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