Question

How many 4 input mux are needed to implement 256 input mux?

Answer 1

4 Lines____4* (1/8)=(1/2) MUXs
As we know ,we have no option rather than 8:1

Hence,total no. of MUXs required to constant  256 : 1 MUX =( 32 + 4 + 1 ) 
                                                                                               =37 MUXs.


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Answer 2

The number of 4 input mux that are needed to implement 256 input mux is 85.

One 4 input mux can cover 4 lines

⇒ 4 lines can be covered by 1 mux

⇒ 1 line can be covered by (1/4) mux

As we know 256 input mux will contain 256 lines of input. Therefore, we have to cover all these lines with 4 input mux.

1 line cover (1/4) mux

⇒ 256 lines cover ((1/4)*256) = 64 mux

Now, these 64 mux will give one output each, and then in the next level we will have 64 lines to cover using 4 input mux.

⇒ 64 lines cover ((1/4)*64) = 16 mux

Similarly, next level we will have 16 lines to cover using 4 input mux

⇒ 16 lines cover ((1/4)*16) = 4 mux

Lastly, next level we will have 4 lines to cover using 4 input mux

⇒ 4 lines cover ((1/4)*4) = 1 mux

Hence, total no of mux's required to construct 256 input mux = (64+16+4+1) = 85 mux's

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