Discrete Mathematics Multiple Choice Questions 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
Answer: c
Clarification: 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.
2. How many cells are there for an 8-variable K-Map?
a) 421
b) 1048
c) 256
d) 375
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: b
Clarification: 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
Answer: d
Clarification: 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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
Answer: b
Clarification: 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.