1-to-8 Multiplexer

A multiplexer is a digital circuit that allows multiple input signals to be combined into a single output signal. The selection of which input to pass through to the output is controlled by a set of control signals. In a 1-to-8 multiplexer, there are 8 input signals and 3 control signals.

Working of a 1-to-8 Multiplexer

A 1-to-8 multiplexer has 8 input lines, denoted as D0 to D7, and 3 control signals, denoted as S0, S1, and S2. The control signals determine which input signal is selected and passed through to the output. The output signal is denoted as Y.

The control signals are typically binary in nature, and they can have 2^3 = 8 possible combinations. Each combination corresponds to one of the 8 input signals being selected as the output.

Using AND Gates

To implement a 1-to-8 multiplexer using AND gates, we can use a combination of AND gates and OR gates. The number of AND gates required depends on the number of input signals and control signals.

For a 1-to-8 multiplexer:
- We have 8 input signals, so we need to consider 8 possible combinations of the control signals.
- Each combination requires 8 AND gates, where each AND gate has two inputs - one from the corresponding input signal and one from the control signal.
- The outputs of these 8 AND gates are then fed into a set of 8 OR gates, where the output of each OR gate represents one of the possible input signals being selected.

Number of AND gates required

For a 1-to-8 multiplexer, we have 8 input signals and 3 control signals. Each combination of control signals requires 8 AND gates. Therefore, the total number of AND gates required is 8 * 8 = 64.

However, we can simplify this circuit by using a smaller number of AND gates. By observing the truth table of a 1-to-8 multiplexer, we can see that some input signals are always 0 for certain combinations of control signals. These input signals can be directly connected to the inputs of the OR gates without the need for AND gates.

After simplification, we find that 8 AND gates are required for a 1-to-8 multiplexer.

Therefore, the correct answer is option 'C', 8.