What type of Boolean logic circuit is this?
There are only two intermediate signals, so it's relatively easy to break down.  We'll call the left input to the bottom OR gate X and the right input Y.

I'm going to use some shorthand here - NOT = !, AND = &amp;, OR = |.


X = A & B

Y = !B & C


Those two lead into the OR gate that produces D:


D = (A & B) | (!B & C)


Which is the result you came up with, so you are correct.

One application of this logic circuit is to act as a selector:


When B is asserted, then A is output on D, and C is ignored.
When B is de-asserted, then C is output on D, and A is ignored.