The minimized expression of the Boolean function Y(P, Q, R) implemented by the multiplexer (MUX) circuit shown in the figure is
The given problem involves a multiplexer (MUX) circuit implementing a Boolean function Y(P, Q, R). We need to determine the minimized expression for this function.
Let's analyze the MUX circuit step-by-step:
- The first MUX selects inputs based on the select lines P and Q (represented as S_1 and S_0 respectively).
- The inputs to this MUX are 0, 1, 1, and 0, corresponding to 00, 01, 10, and 11 select line combinations.
- This implements the function P \oplus Q (XOR gate), since:
- When P = 0 and Q = 0 or P = 1 and Q = 1, the output is 0.
- When P = 0 and Q = 1 or P = 1 and Q = 0, the output is 1.
- The second MUX uses the output of the first MUX and select line R.
- The second MUX outputs a logical function based on:
- When R = 0, the output is the result from the first MUX, which is P \oplus Q.
- When R = 1, the output is 1.
- Effectively, the second MUX implements a logical OR operation: R + (P \oplus Q).
Thus, the minimized expression of the Boolean function is:
Therefore, the correct answer is:
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?
