I'm having trouble trying to simplify one boolean equation into another (and visa versa).
Why are these Boolean expressions,
A.B + C.(A⊕B) = A.B + C.B + A.C
They have the same truth table but I cannot figure out how one simplifies into the other. Here is what I have attempted so far:
A.B + C.(A⊕B)
A.B + C.(A'.B + A.B') ...XOR equivelent
A.B + C.A'.B + C.A.B' ...distributive
I don't know what else I can do. If I try from the other direction, it still does not work:
A.B + C.B + A.C
A.B + C.(B + A) ...distributive
A.B + C.(A'.B')' ...de Morgan's
I don't know if I'm heading in the write direction. Any advice would be appreciated.