Question

Minimum number of 2 × 1 multiplexers required to realize the following function,

f =A̅ B̅ C + A̅ B̅ C̅.

Assume that inputs are available only in true form and Boolean a constant 1 and 0 are available. 

1. 1
2. 2
3. 3
4. 7

Answer 1

Correct Answer - Option 2 : 2

The correct answer is option 2:

 f = A̅ B̅ C + A̅ B̅ C̅

f = A̅ B̅  (C + C̅)

f =  A̅ B̅ = \(\overline{(A + B)}\)

1^st MUX:

I₀ = B and I1 = 1 where A is the select line

Output = A̅.B+ A = A + B

2nd MUX:

I0 = 1 and I1 = 0 where A + B (output of MUX 1) is the select line

Output = \(\overline{(A + B)}\)

Therefore two 2 : 1 mux is needed