## K-map Viva Questions

K-map Viva Questions, Viva Questions on K-map, Viva Questions on Quine-McClusky, Quine-McClusky Viva Questions, Digital Electronics Viva Questions, Engineering Viva Questions, Minimization of Switching Functions, K-map Viva Questions, Short Questions on K-map, Karnaugh map (K-Map) Viva Questions, Karnaugh map Viva Questions

Programmable Logic Devices Viva Questions

### Short Questions and Answers

**Q.1.** *What is a K-map? What are its advantages and disadvantages?*

**Ans.** The K-map is a chart or a graph composed of an arrangement of adjacent cells, each representing a particular combination of variables in a sum or product term. Or simply we can say a K-map is a mapping technique used to minimize logical expression. The advantages of K-map are It is a systematic method of simplifying the Boolean expressions and it is very simple. The disadvantage is that it becomes tedious for problems involving five or more variables and also this method cannot be programmed.

**Q.2.** *Why is the minimization of switching functions required?*

**Ans.** Minimization of switching functions is required in order to reduce the cost of the circuitry (using contact or gate networks) according to some prescribed cost criterion. Realization with minimal expressions also reduces complexity and improves reliability.

**Q.3.** *What is a literal?*

**Ans.** A literal is any variable appearing in the expression in complemented or un-complemented form.

**Q.4.** *What is meant by the SOP form?*

**Ans.** SOP form is one in which each term of the logical expression is a logical product (AND) of some literals and all the terms are logically added (OR).

**Q.5.** *What is meant by POS form?*

**Ans.** POS form is one in which each term of the logical expression is a logical sum (OR) of some literals and the terms are logically multiplied (AND).

**Q.6.** *How many cells an n variable K-map can have?*

**Ans.** An n variable K-map can have 2^{n} cells or squares.

**Q.7.** *What is a standard SOP form?*

**Ans.** A standard or canonical or expanded SOP form is one in which each one of the product terms contains all the variables of the expression either in complemented or non-complemented form. Or a standard SOP form is one in which the logic expression consists of only minterms.

**Q.8.** *What is a standard POS form?*

**Ans.** A standard or canonical or expanded POS form is one in which each one of the sum terms contains all the variables of expression either in complemented or non-complemented form. Or a standard POS form is one in which the logic expression consists of only max terms.

**Q.9.** *What are minterms?*

**Ans.** Each one of the product terms in the canonical SOP form is called a minterm, *i.e.* a minterm is a product term that contains all the variables of the function either in complemented or non-complemented form. Or a minterm is a term containing literal corresponding to all the variables in the ANDed form.

**Q.10.** *What is a maxterm?*

**Ans.** Each one of the sum terms in the canonical POS form is called a maxterm, i.e. a maxterm is a sum containing all variables of the expression either in complement or no-complemented form. Or a maxterm is a term containing literal corresponding to all the variables in ORed form.

**Q.11.** *How do you convert a standard SOP form into a standard POS form?*

**Ans.** A standard SOP form can always be converted into a standard POS form by locating the missing minterms of the SOP form as the maxterms of the POS form.

**Q.12.** *How do you convert a standard POS form into a standard SOP form?*

**Ans.** A standard POS form can always be convened into a standard SOP form by treating the missing maxterms of the POS form as the minterms of the SOP form.

**Q.13.** *When can two minterms or maxterms be combined?*

**Ans.** Two minterms or maxterms can be combined only when they are adjacent to each other.

**Q.14.** *What is a subcube?*

**Ans.** Each square or rectangle made up of a bunch of adjacent minterms or maxterms is called a subcube.

**Q.15.** *When are two squares on a K-map adjacent to each other?*

**Ans.** Two squares on a K-map are said to be adjacent to each other if they are physically adjacent to each other or can be made adjacent to each other by wrapping around.

**Q.16.** *The binary number designations of the rows and columns of the K-map are in which code? Why?*

**Ans.** The binary number designations of the rows and columns of the K-map are in the Gray code. This is to ensure that two physically adjacent squares are really adjacent, i.e. their minterms or maxterms differ by only one variable.

**Q.17.** *What is adjacency ordering?*

**Ans.** Keeping the binary number designations of the rows and columns in Gray code is called adjacency ordering.

**Q.18.** *What is the main criterion in the design of digital circuits?*

**Ans.** The main criterion in the design of digital circuits is the cost (indicated by the number of gate inputs) which must be kept to a minimum.

**Q.19.** *What do you mean by real minimal expression?*

**Ans.** A real minimal expression is the minimal of the SOP and POS expressions.

**Q.20.** *What is a prime implicant in K-map?*

**Ans.** The bunch of 1s on the K-map which form a 2-square, 4-square, etc. is called a Prime implicant or subcube. It is called true prime implicant.

**Q.21.** *What is an essential prime implicant?*

**Ans.** The prime implicant which contains at least one 1 which cannot be covered by any other prime implicant is called an *essential prime implicant*.

**Q.22.** *What is a redundant prime implicant?*

**Ans.** The prime implicant whose each 1 is covered by at least one EPI is called a redundant prime implicant (RPI).

**Q.23.** *What is a selective prime implicant?*

**Ans.** A prime implicant that is neither an essential prime implicant nor a redundant prime implicant is called a selective prime implicant (SPI).

**Q.24.** *What is a False prime implicant?*

**Ans.** The prime implicant made up of a bunch of 0s is called a *False prime implicant*.

**Q.25.** *What are “don’t cares”?*

**Ans**. Combinations for which the value of the expression is not specified are called “don’t care” combinations.

**Q.26.** *What are incompletely specified expressions?*

**Ans. **Incompletely specified expressions are those which are not specified for certain combinations.

**Q.27.** *What is two-level logic? What is its advantage?*

**Ans.** Two-level logic is one in which each input signal passes through two gates to reach the output. The SOP and POS forms of realization give two-level logic. It provides uniform propagation delay between the input and the output but may not yield the real minimal.

**Q.28.** *What is hybrid logic? What is its advantage, disadvantage?*

**Ans.** Hybrid logic is one in which different input signals pass through different numbers of gates to reach the output. The advantage is it results in a circuit with the least number of gate input, so the cost will be less. The disadvantage is that it does not produce uniform time delay and may suffer from the problem of logic race.

**Q.29.** *What do you mean by looping?*

**Ans.** The combining of adjacent squares in a K-map containing 1s (or 0s) for the purpose of simplification of an SOP (or POS) expression is called looping.

**Q.30.** *What is the variable mapping technique? What is its advantage?*

**Ans.** Variable mapping (variable entry mapping) technique is a technique used to minimize the given Boolean expressions which involve infrequently used variables. The advantage is it allows us to reduce a large mapping problem to one that uses just a small map.

**Q.31.** *What is the Quine-McClusky method?*

**Ans.** The Quine-McClusky method also known as the tabular method is a systematic method for minimizing functions of a large number of variables.

**Q.32.** *What is the advantage of the tabular method?*

**Ans.** The advantage of the tabular method is that it is fully algorithmic and hence programmable.

**Q.33.** *What do you mean by the index of a term?*

**Ans.** The index of a term indicates the total number of 1s present in that term. It is also called the weight of the term.

**Q.34.** *In the tabular method, why cannot two terms whose codes differ by a power of 2 but have the same index be combined?*

**Ans.** Two terms whose codes differ by a power of 2 but have the same index cannot be combined since they differ by more than one variable.

**Q.35.** *What are prime implicants in the tabular method?*

**Ans.** The terms which cannot be combined further in the tabular method are called prime implicants. These terms may occur in the final expression.

**Q.36.** *What are essential prime implicants?*

**Ans.** *Essential prime implicants* are the prime implicants that will definitely occur in the final expression. Each essential prime implicant will cover at least one minterm which is not covered by any other prime implicant.

**Q.37.** *What is a prime implicant chart?*

**Ans.** The prime implicant chart is a pictorial representation of the relationships between the prime implicants and the minterms of the expression.

**Q.38.** *How are “don’t care” minterms and maxterms used in the tabular method?*

**Ans.** “Don’t care” minterms and maxterms are used in the table only to obtain the set of prime implicants. They are not used in the prime implicant chart to obtain the essential prime implicants.

**Q.39.** *When do you say that one column is dominating any other column?*

**Ans.** Any column in a prime implicant chart is said to dominate any other column if the first column has a x in every row in which the second column has a x.

**Q.40.** *Which rows and columns can be removed while drawing the reduced prime implicant chart?*

**Ans.** All dominating columns and dominated rows can be removed while drawing the reduced prime implicant chart.