Implementation of 16 to 1 multiplexer using 4 to 1 multiplexers

To implement a 16 to 1 multiplexer, we can use smaller 4 to 1 multiplexers. Let's see how many 4 to 1 multiplexers are required to implement a 16 to 1 multiplexer.

Breaking down the problem

- A 16 to 1 multiplexer has 16 input lines and 1 output line.
- A 4 to 1 multiplexer has 4 input lines and 1 output line.
- We need to use 4 to 1 multiplexers to implement a 16 to 1 multiplexer.
- We can use a hierarchy of multiplexers to implement a larger multiplexer using smaller ones.

Using a hierarchy of multiplexers

- To implement a 16 to 1 multiplexer using 4 to 1 multiplexers, we can use a hierarchy of multiplexers.
- We can first use 4 to 1 multiplexers to implement a 4 to 1 multiplexer.
- Then we can use four of these 4 to 1 multiplexers to implement a 16 to 1 multiplexer.

Calculation

- To implement a 4 to 1 multiplexer, we need 1 4 to 1 multiplexer.
- To implement a 16 to 1 multiplexer, we need four 4 to 1 multiplexers to implement the first stage and 1 4 to 1 multiplexer to implement the second stage.
- Therefore, we need a total of 5 4 to 1 multiplexers to implement a 16 to 1 multiplexer.

Conclusion

- To implement a 16 to 1 multiplexer, we need a hierarchy of multiplexers using 4 to 1 multiplexers.
- We need four 4 to 1 multiplexers to implement the first stage and 1 4 to 1 multiplexer to implement the second stage.
- Therefore, we need a total of 5 4 to 1 multiplexers to implement a 16 to 1 multiplexer.