$f1$(a, b, c) = $\sum(1, 2 ,3,4)$ and $f2$(a, b, c) = $\sum(0, 2, 4, 6)$
Now, $f1\bigoplus f2$ says that
if $f1$ is $true$ then $f2$ must be $false$.
$and$
if $f2$ is $true$ then $f1$ is $false$.
So, all those minterms where both $f1$ and $f2$ are True should not appear or be True for $f1\bigoplus f2$
Because, $f1\bigoplus f2$ will be true only for those minterms for which either $f1$ or $f2$ (not both) are True.
Hence,
Minterm |
$f1$ |
$f2$ |
$f1 \bigoplus f2$ |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
2 |
1 |
1 |
0 |
3 |
1 |
0 |
1 |
4 |
1 |
1 |
0 |
6 |
0 |
1 |
1 |
And for all other minterms $f1$ and $f2$ are $False$.
So, $f1 \bigoplus f2$ = $\sum(0, 1, 3, 6)$