This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Algebra – Prime Implicants and Essentials”.

1. What is the maximum number of prime implicants with 34-variable minimized expression?

a) 34

b) 764

c) 2^{33}

d) 2^{31}

View Answer

Explanation: For n-variable K Map, we have = 2

^{n-1}prime implicants. In this case, n=34 and the maximum number of prime implicants will be 2

^{34-1}= 2

^{33}.

2. How many cells are there for an 8-variable K-Map?

a) 421

b) 1048

c) 256

d) 375

View Answer

Explanation: Any Boolean expression or a function comprising of 8 variables can be solved using an 8-variable K-Map. So, an 8-variable K-Map must contain 2

^{8}= 256.

3. Determine the number of essential prime implicants of the function f(a, b, c, d) = Σm(1, 3, 4, 8, 10, 13) + d(2, 5, 7, 12), where m denote the minterm and d denotes the don’t care condition.

a) 2^{3}

b) 3

c) 643

d) 128

View Answer

Explanation: A prime implicant that cannot be replaced by any other implicant for getting the output is called the essential prime implicants. Here, we have 3 essential prime implicants by using the K-map representation.

4. How many number of prime implicants are there in the expression F(x, y, z) = y’z’ + xy + x’z.

a) 7

b) 19

c) 3

d) 53

View Answer

Explanation: An implicant of a function is a product term which is included in the function.

Hence, for the given function, y’z’, xy and x’z all are prime implicants.

5. f(x, y, z) = xy’+yz’+xyz, what are essential prime implicants of this switching function?

a) 8

b) 0

c) 4

d) 3

View Answer

Explanation: There are no essential prime implicants for this switching function. We can get this solution by using K-Map.

6. How many essential prime implicants are there in the K-Map of the function F = Σ(0, 1, 2, 4, 7, 11, 12, 13, 15)?

a) 4

b) 1

c) 3

d) 7

View Answer

Explanation: By, solving the minimization expression using K-Map, there is only 1 essential prime implicant exist as it is not covered by any other input variable.

7. Determine the number of prime implicants of the following function F?

**F(a, b, c, d) = Σm(1, 3, 7, 9, 10, 11, 13, 15)**

a) 621

b) 187

c) 3^{5}

d) 5

View Answer

Explanation: There are 5 prime implicants for the function (a+b+d’)(a+c’+d’)

(a’+c+d)(a’+b+d’)(a’+b’+c’+d). Hence, the required answer is 5.

8. For an 18-variable k-map determine the number of prime implicants?

a) 2^{18}

b) 35

c) 253

d) 721

View Answer

Explanation: The maximum number of implicants for the n-variable k-map is 2

^{n}. Hence, the required answer is 2

^{18}.

9. How many false essential prime implicants for the given Boolean functions f(A, B, C) = ∑m(2, 5, 6)?

a) 1024

b) 2

c) 16

d) 435

View Answer

Explanation: There are two essential prime implicants such as (B+C) and (B+C’) for the given function. Hence, the required answer is 2.

10. How many minimal forms are there in the function F(A, B, C) = ∑(1, 3, 2, 5, 6, 7) if it is having cyclic prime implicants k-map?

a) 216

b) 2

c) 14

d) 82

View Answer

Explanation: In cyclic prime implicant, min terms will be (1, 3, 5, 7, 9, 11). Hence, either we can have [(1,3), (7,11), (5,9)] or [(1,5), (11,9), (3.7)]. So, there can be 2 minimal forms.

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