The switching function for a Boolean expression is the number of times the output changes from 0 to 1 or from 1 to 0 as the input variables change from one combination to another.
The Boolean expression for f(A, B, C, D) = BD + B'D' can be simplified using Boolean algebra as follows:
f(A, B, C, D) = BD + B'D' = BD + B'(B + D) = BD + B'B + B'D = BD + B'D
Now, let's create a truth table for f(A, B, C, D):
A |
B |
C |
D |
f(A,B,C,D) |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
From the truth table, we can see that the output of the function changes only twice, from 0 to 1 and from 1 to 0. Therefore, the switching function for f(A, B, C, D) is 2.