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How many $2$-input multiplexers are required to construct a $2^{10}$ input multiplexer?

1. $1023$
2. $31$
3. $10$
4. $127$

Given MUX = 2 x 1

Required MUX = 2^10 x 1 = 1024 x 1

Now, there is a shortcut technique to find out the the number of MUX required which is,

No. of MUX = Required input / Given input

Now, required input to the MUX is 1024 and given input to the MUX is 2. We will have to keep on dividing required input with given input i.e 1024 / 2 = 512

512 / 2 = 256

256 / 2 = 128

128 / 2 = 64

64 / 2 = 32

32 / 2 = 16

16 / 2 = 8

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1

Now, we have to add up all the results i.e (512+256+128+64+32+16+8+4+2+1) = 1023

Hence, the no. of MUX required is 1023