How many 2-input multiplexers are required to construct a 2¹⁰-input multiplexer?
(A) 1023
(B) 31
(C) 10
(D) 127


Answer: (A)

Explanation: Consider that we need to create 210 input multiplexer using 2-input multiplexers.

In the first level, we need to organize 29 Multiplexers which will accept 2-inputs each (hence 210 Inputs in total) & gives out 1 output each (hence 29 outputs in total).
In the second level, we need to organize 28 Multiplexers which will accept 2-inputs each (hence 29 Inputs in total) & gives out 1 output each (hence 27 outputs in total) and so on.
In the tenth level, we need to organize 1 Multiplexer which will accept 2-inputs & gives out 1 output.

Total number of 2×1 MUX needed = 2⁹ + 2⁸ + 2⁷ + … + 2² + 1 = 1023

So, option (A) is correct.

Quiz of this Question