Minimum number of multiplexers required to realize the following function, f =…

Given:

f = A'B'C + A'B'C'

We can factor out the common terms A'B':

f = A'B'(C + C')

Since (C + C') = 1 according to Boolean identity:

f = A'B'

2. Implementation using 2-to-1 MUX

Since the inputs are available only in true form (A, B, C), we cannot directly use A' or B'. We must use the multiplexers to generate the necessary complements or the logic function itself.

A 2-to-1 MUX performs the function: Y = S'I_0 + SI_1 (where S is the select line).

Step 1: Generate A'

To get A' using a 2-to-1 MUX with only true forms available:

• Select line (S) = A

• I_0 = 1

• I_1 = 0

• Result: A(0) + A'(1) = f{A'}

Step 2: Realize f = A'B'

Now we use a second MUX to implement the AND logic between A' and B':

• Select line (S) = B

• I_0 = A' (output from the first MUX)

• I_1 = 0

• Result: B(0) + B'(A') = f{A'B'}

3. Conclusion

To realize the function f = A'B' using only true inputs:

1. One MUX is needed to act as an inverter to create A'.

2. One MUX is needed to perform the AND operation with B'.

Minimum number of 2-to-1 MUX required = 2.