ISRO2008-22

Question

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

• A. $1023$
• B. $31$
• C. $10$
• D. $127$

Answer 1

1023
1st level 512 MUX
2nd level 256 MUX
.
.
So on
Total= 512+256+128+64+32+16+8+4+2+1=1023 MUX

Comments

This video helps:

https://www.youtube.com/watch?v=Qp1q2zuGXdk

Answer 2

The No of 2 input Mux required =2ⁿ -1

                                                 =2¹⁰ -1

                                                 =1023

Comments

is 2^n -1 can be applied to all cases to find no of MUX or decoders needed?

---

2$\times$1 MUX only

Answer 3

Number of N input MUXs required to make M input MUX is = ceil (M-1 / N-1)

In given question,

no of MUX needed = 2 ¹⁰ -1 /2-1 = 1023/1 =1023

Answer 4

Levels of Multiplexers:

• Level 1: Use $2^9$ 2-input multiplexers to select between 2^9 pairs of inputs.
• Level 2: Use $2^8$ 2-input multiplexers to select between the outputs of pairs of Level 1 multiplexers, resulting in $2^8$ selected inputs.
• Level 3: Repeat the process with $2^7$ multiplexers, then $2^6$, and so on, until reaching a single multiplexer at the top level.

Total Multiplexers:

• Sum up the number of multiplexers at each level:
  • $2^9$ + $2^8$ + $2^7$ + ... + $2^1$ + $2^0$ $=$ $2^{10}$ - $1$ $=$ $1024 - 1$ $=$ $1023$