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Discrete Mathematics | Karnaugh Maps MCQs

Discrete Mathematics | Karnaugh Maps MCQs: This section contains multiple-choice questions and answers on Karnaugh Maps in Discrete Mathematics.
Submitted by Anushree Goswami, on October 28, 2022

1. Karnaugh maps are planar areas divided into ____ equal cells, each representing a point for a function of n variables.

1. 2ⁿ
2. 2ⁿ⁺¹
3. 2^n-1
4. 2

Answer: A) 2ⁿ

Explanation:

Karnaugh maps are planar areas divided into 2ⁿ equal cells, each representing a point for a function of n variables.

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2. There are two variables called x, one for x and another for x', which are used to divide the area into ____ equal halves.

1. Two
2. Three
3. Four
4. Multiple

Answer: A) Two

Explanation:

There are two variables called x, one for x and another for x', which are used to divide the area into two equal halves.

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3. A cell corresponding to an argument with the value 1 contains a ____ data point.

1. Single
2. Double
3. Triple
4. Multiple

Answer: A) Single

Explanation:

A cell corresponding to an argument with the value 1 contains a single data point.

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4. It is possible to simplify Boolean Functions with ____-maps.

1. K
2. L
3. M
4. N

Answer: A) K

Explanation:

It is possible to simplify Boolean Functions with k-maps.

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5. Term combinations are made by placing ____ cells next to each other.

1. Adjacent
2. Complimentary
3. Supplementary
4. Nodes

Answer: A) Adjacent

Explanation:

Term combinations are made by placing adjacent cells next to each other.

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6. When only ____ variable differs between two cells, they are said to be adjacent.

1. Three
2. Two
3. One
4. Multiple

Answer: C) One

Explanation:

When only one variable differs between two cells, they are said to be adjacent.

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7. One variable is the same in adjacent cells, while the other variable appears ____ in one and complemented in the other.

1. Complemented
2. Un-complemented
3. Both A and B
4. None of the above

Answer: B) Un-complemented

Explanation:

One variable is the same in adjacent cells, while the other variable appears un-complemented in one and complemented in the other.

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8. Minimization of the SOP Form can be done in the following steps -

1. Encircle the ones that cannot be combined with any others.
2. Encircle the ones that can be grouped together only one way in groups of two.
3. In groups of four adjacent ones, identify the ones which can be combined with three others and encircle them.
4. Identify the eight adjacent ones that can be combined with seven others, in only one way, and encircle them.
5. The remaining 2, 4, and 8 essential groups should be combined with each other or with other already encircled groups if there are any that have not been encircled.

Select the correct order -

1. i > ii > iii > iv > v
2. i > ii > iv > ii > v
3. i > iv > ii > iii > v
4. i > v > ii > iii > iv

Answer: A) i > ii > iii > iv > v

Explanation:

Minimization of the SOP Form can be done in the following steps -

1. Encircle the ones that cannot be combined with any others.
2. Encircle the ones that can be grouped together only one way in groups of two.
3. In groups of four adjacent ones, identify the ones which can be combined with three others and encircle them.
4. Identify the eight adjacent ones that can be combined with seven others, in only one way, and encircle them.
5. The remaining 2, 4, and 8 essential groups should be combined with each other or with other already encircled groups if there are any that have not been encircled.

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9. Minimizing such functions can be achieved by converting them into standard forms such as ____, then making the k-map and obtaining the minimized function.

1. SOP
2. POS
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Minimizing such functions can be achieved by converting them into standard forms such as SOP or POS, then making the k-map and obtaining the minimized function.

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10. Algorithm to prepare the K-map -

1. You should enter one for the minimum term and zero for the maximum term.
2. Ones/zeroes should be entered for each term with one fewer variable than the total.
3. In a similar manner, repeat for other terms.
4. When there are fewer than two variables in the term, enter four adjacent one's/zeroes.

Select the correct order -

1. ii > i > iv > iii
2. i > ii > iii > iv
3. i > iv > ii > iii
4. i > ii > iv > iii

Answer: D) i > ii > iv > iii

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