Choose any images you like and make a list in v, then make a vertices list. Be careful if you like to use two different instances of the same shape you need to call Property twice e.g. see Property[3,VertexShape->v[[3]]], Property[4,VertexShape->v[[3]]]:

v={,,};
vertices={Property[1,VertexShape->v[[1]]],Property[2,VertexShape->v[[2]]],Property[3,VertexShape->v[[3]]], Property[4,VertexShape->v[[3]]]};

Then build your boolean circuit as you like. However note that it will not be like an electrical circuit drawn in textbooks, that is hard for us to do now, maybe later on, but for now you could use this...

g=Graph[vertices,{1->2,3->2,2->4},VertexSize->0.4,DirectedEdges->True, GraphLayout->"SpringElectricalEmbedding"]

This does a full syntax parse of a boolean expression, kinda hard but useful for some situations.

TreeForm[p ∧ q ∨¬ r∧q∨¬(r∧¬s),DirectedEdges-> True,ImageSize->600]/.{Or->, And->,Not->}