Logic functions and Minimization

Question 21

Consider the following circuit. Which one of the following is TRUE?

• f is independent of X
• f is independent of Y
• f is independent of Z
• None of X, Y, Z is redundant

Question 22

The switching expression corresponding to f(A, B, C, D) = Σ (1, 4, 5, 9, 11, 12) is

• BC\'D\' + A\'C\'D + AB\'D

• ABC\' + ACD + B\'C\'D

• ACD\' + A\'BC\' + AC\'D\'

• A\'BD + ACD\' + BCD\'

Question 23

The Boolean function x\'y\' + xy + x\'y is equivalent to

• x\' + y\'
• x + y
• x + y\'
• x\' + y

Question 24

Given f(x, y, w, z) = Σm(0, 1, 2, 3, 7, 8, 10) + Σd(5, 6, 11, 15), where d represents the don\'t-care condition in Karnaugh maps. Which of the following is a minimum sum of products (SOP) form of f(x, y, w, z)?

• f = y\'z\' + x\'y\' + wz

• f = w\'z\' + w\'x\' + yz

• f = y\'z\'+x\'z

• f = (y\' + z\' )( w\' + z )

Question 25

Which are the essential prime implicants of the following Boolean function? f(a, b, c) = a\'c + ac\' + b\'c

• a\'c and ac\'
• a\'c and b\'c
• a\'c only
• ac\' and bc\'

Question 26

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"

[caption width="800"] [/caption]

• (11, 9)

• (9, 13)

• (9, 10)

• (11, 11)

Question 27

Consider the following circuit composed of XOR gates and non-inverting buffers. The non-inverting buffers have delays d1 = 2 ns and d2 = 4 ns as shown in the figure. Both XOR gates and all wires have zero delay. Assume that all gate inputs, outputs and wires are stable at logic level 0 at time 0. If the following waveform is applied at input A, how many transition(s) (change of logic levels) occur(s) at B during the interval from 0 to 10 ns ?

• 1
• 2
• 3
• 4

Question 28

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

• xz + y\'z

• xz\' + zx\'

• x\'y + zx\'

• None of these

Question 29

Consider the following logic circuit whose inputs and function and output is f. Given that

f1(dx, y, z) = ∑(0, 1, 3, 5),
f2(dx, y, z) = ∑(6, 7) and
f(dx, y, z) = ∑(1, 4, 5),

f3 is :

• ∑(1, 4, 5)
• ∑(6, 7)
• ∑(0, 1, 3, 5)
• None of these

Question 30

Let f(A, B) = A\' + B. Simplified expression for function f(f(x + y, y)z) is :

• x\' + z
• xyz
• xy\' + z
• None of these