Discrete Mathematics Questions and Answers – Boolean Algebra – Prime Implicants and Essentials

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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) 233
d) 231
View Answer

Answer: c
Explanation: For n-variable K Map, we have = 2n-1 prime implicants. In this case, n=34 and the maximum number of prime implicants will be 234-1 = 233.
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2. How many cells are there for an 8-variable K-Map?
a) 421
b) 1048
c) 256
d) 375
View Answer

Answer: c
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 28 = 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) 23
b) 3
c) 643
d) 128
View Answer

Answer: b
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

Answer: c
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

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

Answer: b
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) 35
d) 5
View Answer

Answer: d
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) 218
b) 35
c) 253
d) 721
View Answer

Answer: a
Explanation: The maximum number of implicants for the n-variable k-map is 2n. Hence, the required answer is 218.

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

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

Answer: b
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn