The implementation of a 4-to-1 multiplexer requires ___________NOT gates.a.3b.4c.1d.2

To determine the number of NOT gates required for the implementation of a 4-to-1 multiplexer, we need to analyze the functionality of the multiplexer itself and which logical gates are involved.

1. Break Down the Problem

• A 4-to-1 multiplexer has 4 input lines (I0, I1, I2, I3) and 2 selection lines (S0, S1) that select one of the 4 inputs to output.
• The selection lines take combinations of 0 and 1 to enable one of the inputs.

2. Relevant Concepts

• In a basic 4-to-1 multiplexer using logic gates:
  • The two selection lines require decoding to determine which input line to connect to the output.
  • A 2-to-4 line decoder is typically used, which can be created using AND gates and NOT gates.

3. Analysis and Detail

• To control the output based on the selection lines (S0 and S1), we can implement the following:

  • The NOT gates are utilized to create the complementary signals needed for the AND gates that will enable the appropriate input.
  • From the truth table of a 4-to-1 multiplexer, it can be observed that we require the inverted forms of the selection inputs.

• For a 4-to-1 multiplexer:

  • S0 can be inverted to S0' using 1 NOT gate.
  • S1 can be inverted to S1' using another NOT gate.

Thus, the total number of NOT gates required is $2$.

4. Verify and Summarize

• The calculations confirm that we need one NOT gate for each of the selection lines.
• Therefore, the total is:

Final Answer

2 NOT gates are required for the implementation of a 4-to-1 multiplexer. Hence, the answer is d. 2.