topic – RBR

Question 1

Consider the minterm list form of a Boolean function F given below.

F(P, Q, R, S) = Σm(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)

Here, m denotes a minterm and d denotes a don’t care term. The number of essential prime implicants of the function F is _______ .

A	3
B	4
C	5
D	6

Digital-Logic-Design K-Map Gate 2018

Question 1 Explanation:

f = Σ(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)

There are 3 prime implicant i.e., P’QS, Q’S’ and PQ’ and all are essential.
Because 0 and 2 are correct by only Q’S’, 5 and 7 are covered by only P’QS and 8 and 9 are covered by only PQ’.

Question 2

Consider the Karnaugh map given below, where X represents “don’t care” and blank represents 0.

Assume for all inputs , the respective complements are also available. The above logic is implemented using 2-input NOR gates only. The minimum number of gates required is _________.

A	1
B	2
C	3
D	4

Digital-Logic-Design K-Map Gate 2017 set-01

Question 2 Explanation:

Given K-Map represents the function f(a, b, c, d) = a' c = a'(c' )' = (a + c')'
As all variables and their complements are available we can implement the function with only one NOR Gate.

Question 3

Given f(w,x,y,z) = Σ_m(0,1,2,3,7,8,10) + Σ_d(5,6,11,15), where d represents the don’t-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w,x,y,z)?

A
B
C
D

Digital-Logic-Design K-Map GATE 2017(set-02)

Question 3 Explanation:

f(w,x,y,z) = Σ_m(0,1,2,3,7,8,10) + Σ_d(5,6,11,15)
K-Map for the function f is

Consider maxterms in K-map to represent function in product-of-sums (POS) form
f(w,x,y,z) = (w' + z')(x' + z)

Question 4

The total number of prime implicants of the function f(w,x,y,z) = Σ(0, 2, 4, 5, 6, 10) is ______.

A	3
B	4
C	2
D	1

Digital-Logic-Design K-Map GATE 2015(Set-03)

Question 4 Explanation:

Total 3 prime implicants are there.

Question 5

What is the minimal form of the karnaugh map shown below? Assume that X denotes a don't care term

A
B
C
D

Digital-Logic-Design K-Map Gate 2012

Question 5 Explanation:

Question 6

In the Karnaugh map shown below, X denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

A
B
C
D

Digital-Logic-Design K-Map Gate-2008

Question 6 Explanation:

Question 7

Consider the following expression ad' + (ac)' + bc'd Which of the following Karnaugh Maps correctly represents the expression?

A

B

C

D

Hence, option (A) matches.

Question 8

Consider the following expression ad' + (ac)' + bc'd Which of the following expressions does not correspond to the Karnaugh Map obtained for the above expression??

A	c’d’+ ad’ + abc’ + (ac)’d
B	(ac)’ + c’d’ + ad’ + abc’d
C	(ac)’ + ad’ + abc’ + c’d
D	b’c’d’ + acd’ + (ac)’ + abc’

Digital-Logic-Design K-Map Gate 2007-IT

Question 8 Explanation:

Let's check for option (C):
a'c' + ad' + abc' + c'd

Not equivalent to the K-map, we get in previous question.

Question 9

Consider a Boolean function f (w, x, y, z). Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i₁ = 〈w₁, x₁, y₁, z₁〉 and i₂ = 〈w₂, x₂, y₂, z₂〉, we would like the function to remain true as the input changes from vectors i₁ to i₂ (i₁ and i₂ differ in exactly one bit position), without becoming false momentarily. Let f(w, x, y, z) = ∑(5, 7, 11, 12, 13, 15). Which of the following cube covers of f will ensure that the required property is satisfied?

A
B
C
D

Digital-Logic-Design K-Map Gate-2006

Question 9 Explanation:

Static hazard is the situation where, when one input variable changes, the output changes momentarily before stabilizing to the correct value. The most commonly used method to eliminate static hazards is to add redundant logic (consensus terms in the logic expression).
f = X₁ * X₂ + X₁' * X₃
If (X₁,X₂,X₃) = (1,1,1) then f=1 because X₁ * X₂ =1 X₁' * X₃ = 0.
Let the input is changed from 111 to 011 , then f = 1 because X₁ * X₂ = 0 X₁' * X₃ =1.
The output f will be momentarily 0 if AND gate X₁ * X₂ is faster than the AND gate X₁' * X3.
This Hazard can be avoided by adding the term X₂ * X₃ (because X₁ is in true form in first term and in complement form in the second term . So pick the fixed terms X₂ and X₃ from both terms) to f i.e f = X₁ * X₂ + X₁' * X₃ + X₂ * X₃
Option D is equivalent to f(w, x, y, z) = ∑(5,7,11,12,13,15)

Question 10

A	a^ȼc and ac^ȼ
B	a^ȼc and b^ȼc
C	a^ȼc only
D	ac^ȼ and bc^ȼ

Digital-Logic-Design K-Map Gate-2004

Question 10 Explanation:

From given function 'f' we can draw,

There are two EPI,
A'C and AC'.

Question 11

The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xy + xz') is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map ? Here, X denotes "don't care"