Digital Logic & Number representation

Question 1

What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term.

[caption width="800"] [/caption]

• b\'d\'

• b\'d\' + b\'c\'

• b\'d\' + a\'b\'c\'d\'

• b\'d\' + b\'c\' + c\'d\'

Question 2

The output of the following combinational circuit is F. The value of F is:

• P₁+P^\'₂P₃
• P₁+P^\'₂P^\'₃
• P₁+P₂P^\'₃
• P^\'₁+P₂P₃

Question 3

A binary 3-bit down counter uses J-K flip-flops, FF_i with inputs J_i, K_i and outputs Q_i, i = 0, 1, 2 respectively. The minimized expression for the input from following, is

• I, III, V

• I, IV, VI

• II, III, V

• II, IV, VI

Question 4

The truth table represents the Boolean function

• X
• X+Y
• X xor Y
• Y

Question 5

In the following truth table, V = 1 if and only if the input is valid. What function does the truth table represent?

• Priority encoder
• Decoder
• Multiplexer
• Demultiplexer

Question 6

Which one of the following expressions does NOT represent exclusive NOR of x and y?

• xy+x\'y\'
• x⊕y\'
• x\'⊕y
• x\'⊕y\'

Question 7

Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate?

• A
• B
• C
• D

Question 8

The simplified SOP (Sum Of Product) form of the boolean expression (P + Q\' + R\') . (P + Q\' + R) . (P + Q + R\') is

• (P\'.Q + R\')
• (P + Q\'.R\')
• (P\'.Q + R)
• (P.Q + R)

Question 9

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. 

[caption width="800"] [/caption]

If at some instance prior to the occurrence of the clock edge, P, Q and R have a value 0, 1 and 0 respectively, what shall be the value of PQR after the clock edge?

• 000

• 001

• 010

• 011

Question 10

Consider the data given in previous question. If all the flip-flops were reset to 0 at power on, what is the total number of distinct outputs (states) represented by PQR generated by the counter?

• 3

• 4

• 5

• 6