MUX conversion to a function

Question

F(A,B,C,D)=$\Sigma$(0,2,3,5,8,10,11,12,15)

Realize it using 8:1  MUX .

what is the logic behind?

Answer 1

Logic is we can make 8 x 1 MUX by using 4 variables, where select lines are 3 (S2, S1, S0) { S2 =A ,S1= B, S0 =C)

D we can get from the inputs.

Comments

this much I also understand but is there any fast method other than making table?

---

See u cannot do this way, It is 2³*1 MUX, we can not implement 4 variable functions with only 8*1 MUX, we need 1 inverter also

---

Is it required in every case (INVERTER)?

---

forget the above question ,

Is it possible to realize 3 variable function by only using  4: 1  MUX ?

---

As I already said we can not implement an n+1 variable function with 2ⁿ_*1 MUX. we need some other gates as well

U can not implement 3 variable function by only 2²_*1 MUX

---

Are you sure about it?

U can not implement 3 variable function by only 2²_*1 MUX

---

Yes 100% sure

---

f(A,B,C)=$\Sigma$m(1,4,5,7)  

try this ?

---

u can try and come to me

---

ok please correct me if I am wrong..

---

Correct me if I am wrong..

---

whatever statement I have said earlier, that is true for general

Here we are lucky in your example that we are able to implement 3 variable function with 2²_*1 MUX but what if we will provide C' at I0 and I3 inputs, then we can not implement it.

here we are implementing 3 variable function with 4*1 MUX but we can not say that we can implement any 3 variable function with 4* 1 MUX

---

so we can't be sure right 

because in option it was given that 

few 3 variables functions are possible 

---

yes