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how many two input multiplexers are required  to construct a 2^(10) input multiplexer?
asked in Digital Logic by Loyal (3.2k points) 2 11 26 | 34 views

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Given we have to realise a 210 : 1 MUX  using  2 : 1 MUX..

At the outermost level i.e. input level , 

No of inputs needed    =    210  [ As the MUX is 210 : 1 ]

So no of 2 : 1 MUX needed at first level   =  210 /  2     =    29

So number of output lines from these MUXes    =    No of MUXes at 1st level   =  29

So no of inputs to 2nd level of MUXes  = No of outputs from 1st level MUXes  =  29

Hence no of 2:1 MUXes needed at 2nd level    =   29 /  2    =    28

Likewise we continue to the last level where the number of MUX  = 1..

Hence number of 2 :1 MUXes needed to realise 210 : 1 MUX.   =    29 + 28 + .......... + 1

                                                                                            =   1(210 - 1) / (2-1)

                                                                                            =    1023

Hence required number of MUXes       =     1023 

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