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 number of control lines in a multiplexer is 5, identify the MUX.
Number of control lines required for 16 to 1 multiplexer is _____
In a multiplexer, the number of input lines is ‘n’ and the number of select lines is ‘m’. Which of the following is correct?
________ is used to carry digital data on analog lines.
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?
