Consider three 4-variable functions f1, f2 and f3, which are expressed in sum-of-minterms f1 = Σ(0, 2, 5, 8, 14)f2 = Σ(2, 3, 6, 8, 14, 15)f3 = Σ(2, 7, 11, 14) For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

Σ(0, 2, 3, 5, 6, 7, 8, 11, 14)

Given the following Karnaugh Map for a Boolean function 𝐹(𝑤, 𝑥, 𝑦, 𝑧):FigureWhich one or more of the following Boolean expression(s) represent(s) 𝐹?

𝑤̅𝑥̅𝑦̅𝑧̅+ 𝑤̅𝑥̅𝑦𝑧̅+ 𝑤𝑥̅𝑦𝑧 +𝑥z

𝑤̅𝑥̅𝑦̅𝑧̅+ 𝑤𝑥̅𝑦̅𝑧̅+ 𝑤𝑥̅𝑦̅𝑧 + 𝑥z

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Question 1

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"

(GATE 2003 | MCQ | 2-mark)

A
(11, 9)
B
(9, 13)
C
(9, 10)
D
(11, 11)

Question 2

Minimum sum of product expression for f(w, x, y, z) shown in Karnaugh-map below is

_yz\\^wx	00	01	11	10
00	0	1	1	0
01	x	0	0	1
11	x	0	0	1
10	0	1	1	x

(GATE 2002 | MCQ | 1-mark)

A
xz + y'z
B
xz' + zx'
C
x'y + zx'
D
None of these

Question 3

Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?

(GATE 2001 | MCQ | 1-mark)

A
xy + y'z
B
wx'y' + xy + xz
C
w'x + y'z + xy
D
xz + y

Question 4

Consider the following Karnaugh map:

xy ↓ / wz →	00	01	11	10
00	0	X	0	0
01	0	X	1	1
11	1	1	1	1
10	0	X	0	0

Which of the following Boolean expressions represents the given K-map?

(GATE 2000 | MCQ | 1-mark)

A
(w+x)y
B
xy +yw
C
(W + X)(W' + Y)(X' +Y )
D
None of the above

Question 5

The number of min-terms after minimizing the following Boolean expression is _________.

      [D′ + AB′ + A′C + AC′D + A′C′D]′

Question 6

Which one of the following circuits implements the Boolean function given below?

f(x,y,z) = m0 + m1 + m3 + m4 + m5 + m6

where mi is the ith minterm.

Question 7

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

g_set1_q18

Assume for all inputs (a, c, d) the respective complements (a', b', c', d')are also available. The above logic is implemented 2-input NOR gates only. The minimum number of gates required is ____________. Note: This questions appeared as Numerical Answer Type.

Question 8

Consider three 4-variable functions f₁, f₂ and f₃, which are expressed in sum-of-minterms

f₁ = Σ(0, 2, 5, 8, 14)
f₂ = Σ(2, 3, 6, 8, 14, 15)
f₃ = Σ(2, 7, 11, 14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

A
Σ(7, 8, 11)
B
Σ(2, 14)
C
Σ(0, 2, 3, 5, 6, 7, 8, 11, 14)
D
Σ(2, 7, 8, 11, 14)

Question 9

What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer ________ .

Note: This was Numerical Type question.

Question 10

Given the following Karnaugh Map for a Boolean function 𝐹(𝑤, 𝑥, 𝑦, 𝑧):

Which one or more of the following Boolean expression(s) represent(s) 𝐹?

𝑤̅𝑥̅𝑦̅𝑧̅+ 𝑤𝑥̅𝑦̅𝑧̅+ 𝑤̅𝑥̅𝑦𝑧̅+ 𝑤𝑥̅𝑦𝑧̅+ 𝑥𝑧
𝑤̅𝑥̅𝑦̅𝑧̅+ 𝑤̅𝑥̅𝑦𝑧̅+ 𝑤𝑥̅𝑦𝑧 +𝑥z
𝑤̅𝑥̅𝑦̅𝑧̅+ 𝑤𝑥̅𝑦̅𝑧̅+ 𝑤𝑥̅𝑦̅𝑧 + 𝑥z
𝑥̅𝑧̅+ 𝑥z

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Digital Logic

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