How many number of 2x1 multiplexers required for design of a 8x1 multiplexer?

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Answer

Number of 2x1 Multiplexers Required to Design an 8x1 Multiplexer

When designing a multiplexer, the goal is to select one output from multiple inputs. A multiplexer with n input lines requires log2(n) select lines. A 2x1 multiplexer has two input lines and one select line. An 8x1 multiplexer has eight input lines and three select lines.

Using 2x1 Multiplexers to Design an 8x1 Multiplexer

To design an 8x1 multiplexer using 2x1 multiplexers, we can use the following steps:

Use two 2x1 multiplexers to select between four inputs each. This will result in two outputs.

Use another 2x1 multiplexer to select between the two outputs from step 1. This will result in one output.

So, a total of three 2x1 multiplexers are required to design an 8x1 multiplexer using 2x1 multiplexers.

Advantages and Disadvantages of Using 2x1 Multiplexers

Using 2x1 multiplexers to design a larger multiplexer has the following advantages and disadvantages:

Advantages

2x1 multiplexers are widely available and inexpensive.

Using 2x1 multiplexers makes it easier to design more complex multiplexers.

2x1 multiplexers can be cascaded to design larger multiplexers.

Disadvantages

Using multiple 2x1 multiplexers can increase the propagation delay of the overall circuit.

Using multiple 2x1 multiplexers can increase the complexity of the circuit.

Overall, using 2x1 multiplexers to design a larger multiplexer is a viable option, but it is important to consider the advantages and disadvantages before deciding on a particular design approach.

Answer

To implement 2^n x 1 mux using 2x1 mux ... the total no of 2x1 mux needed are ... :: (2^n) - 1....

that mean for the given question...

8x1 mux can be rewritten as 2^3 x 1 mux ... so n value is 3....
then the required answer is .... (2^3) - 1 = 7 ....

the answer for the question is ..: 7

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