multiplexer

Question

by using a 8 * 1 MUX if 4 variable function is realized then the circuit is ?

(a) unique circuits

(b) 2 possible circuits

(c) multiple possible circuits

(d) not possible to realise the boolean function

Comments

https://gateoverflow.in//1232/gate2007_34

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ANSER IS C BECAUSE ANY ONE OUT OF A,B,C,D COULD BE USED AS SELECT LINE

Answer 1

Ans -(c) Multiple possible circuit

 we have a 8*1 Mux and a 4 variable boolean function(say w,x,y,z) .So , to implement a 4 variable boolean function by using a 8*1 mux

1.>we need to apply any three of the  input to the three selection line of mux which can be done in 24 ways.(The first selection line s₀ can be w or x or y or z and in the same way s₁ has 3 possibilty ,s₂ has 2 possibilty

total combination=4ways *3ways*2ways=24ways)

2.>The remaining one input will be adjusted in the 8 input line.

so,for each possible combination out of those 24 combination we will get a completly different ckt but the functionality of all thesr ckt will be same. 

Answer 2

The ans is A - unique circuit (only a not gate required )

the question is saying With a single 8:1 mux how to convert a 16:1 mux .......  we can manage the extra variable D (say four variables are A B C D ) by putting D according to the function in the input line of 4:1 mux and there are 2 possibility either D or D' .  for this we need a extra not gate .

if the Question would be like this "by using 8 * 1 MUX if 4 variable function is realised than the circuit is ?"

then the answer will be like :

8:1 MUX means it can support (with only one 8:1 MUX) 3 variables ,the input line will be 8 , select lines are 3 (variables) and one output line. and now 16:1 MUX it can support (with only one 16:1 MUX) 4 variables ,the input line will be 16 , select lines are 4 (variables) and one output line.

So the question can be converted like this .... how many 8:1 MUX is needed to build a 16:1 MUX !!!

and i assume you know how to calculate it  ..... upper ceiling ( (16/8) + (16/8^2) )  = 3

3 8:1 MUX is required .

Comments

yeah i know . instead of taking taking 16:1 MUX using 8:1 I  used 8:1 MUX  using 4:1  MUX for simplification

. Both cases are same and smaller examples are easy to understand , easy to implement and take less space and I am little bit lazy :P . peace

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now wt is the conclusion about this question...!! and what is the final answer..??

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The answer for this question is A . Only one circuit is required (only a not gate ) .

Answer 3

by using "A" 8 * 1 MUX ... // word 'A' matters
We need additional NOT GATE with a 8*1 mux to implement 4 variable function..
Unique circuit..

Comments

i think it should take a unique circuit because there would be three select line one variable will left for input line so we need only not gate to take complement that variable