To obtain the Boolean function $F(X,Y) = X\bar{Y} + \bar{X}$, the inputs PQRS in the figure should be
To determine the correct inputs PQRS for the Boolean function F(X, Y) = X\bar{Y} + \bar{X}, we will analyze the behavior of the given function using the multiplexer configuration.
The figure shows a 4:1 multiplexer with two select lines S1 and S0, which are connected to X and Y respectively, and inputs P, Q, R, and S corresponding to the input lines when select lines have different values:
- Select lines S1 and S0 correspond to X and Y respectively.
- The selection of inputs is as follows:
- S1S0 = 00: Selects input P
- S1S0 = 01: Selects input Q
- S1S0 = 10: Selects input R
- S1S0 = 11: Selects input S
The Boolean function F(X, Y) = X\bar{Y} + \bar{X} should be realized as per the settings:
- When XY = 00 (i.e., S1S0 = 00), F = \bar{X}. Here, P = 1.
- When XY = 01 (i.e., S1S0 = 01), F = \bar{X}. Here, Q = 1.
- When XY = 10 (i.e., S1S0 = 10), F = X\bar{Y}. Here, R = 1.
- When XY = 11 (i.e., S1S0 = 11), F = 0. Here, S = 0.
Thus, the required inputs PQRS for realizing the function F(X, Y) = X\bar{Y} + \bar{X} are 1110.
Hence, the correct option is: 1110.
Important Questions from Multiplexer
The device which changes from serial data to parallel data is:
Consider a logic gate circuit. with 8 input lines (D 0, D 1..... D 7) and 3 output lines (A 0, A 1, A 2) specified by following operations
A 2= D 4+ D 5+ D 6+ D 7
A 1= D 2+ D 3+ D 6+ D 7
A 0= D 1+ D 3+ D 5+ D 0
Where + indicates logical OR operation. This circuit is
Which of the following statements are true?
A. Frequency division multiplexing technique can be handled by digital circuits.
B. Time division multiplexing technique can be handled by analog circuits
C. Wavelength division multiplexing technique is used with optical fiber for combining two signals.
D. Frequency division multiplexing technique can be applied when the bandwidth of a link is greater than the bandwidth of the signals to be transmitted.
Choose the correct answer from the options given below :
Consider the sentence below.
There is a country that borders both India and Pakistan.
Which of the following logical expressions express the above sentence correctly when the predicate Country(x) represents that x is a country and Borders(x, y) represents that the countries x and y share the border?
A digital computer has a common bus system for 8 registers 16 bits each. How many multiplexers are required to implement common bus? What size of multiplexers is required?
