The Boolean expression of the output f of the multiplexer shown below is:

[4:1 MUX with select lines P (MSB) and Q (LSB...

Question

The Boolean expression of the output f of the multiplexer shown below is:

[4:1 MUX with select lines P (MSB) and Q (LSB), data inputs: I0=0, I1=1, I2=R, I3=R']

A. P'Q + P(Q XOR R)
B. P + Q XOR R
C. P'Q XOR R
D. P' + Q*R

Accepted Answer

f = P'Q + P(Q XOR R), which is option A. A 4:1 multiplexer selects one of four data inputs based on two select lines. Here P is the MSB select and Q is the LSB select. The four data inputs are 0, 1, R, and R' (complement of R). We need to write the Boolean expression for the output by expanding the MUX truth.

The Boolean expression of the output f of the multiplexer shown below is: [4:1 MUX with select lines P (MSB) and Q (LSB), data inputs: I0=0, I1=1, I2=R, I3=R'] A. P'Q + P(Q XOR R) B. P + Q XOR R C. P'Q XOR R D. P' + Q*R