Hi, I need to design stae diagram of 0110 or 1001 sequence detector which produces a 1 output if one of the following sequence appear
This doesn't seem to be sinking in, so let me be a bit more explicit. This is the Homework Help forum, not the Homework Done For You forum. YOU need to show YOUR best effort to solve YOUR homework problem. That allows US to see what approach you are taking and where you are going right and where you are going wrong and to the guide you along the path while YOU do the work to solve YOUR homework problem.
I know how to draw state diagram for those sequences but don't know how to put those two diagrams into one
It very hard to read your diagram. Once you get something scribbled out and think you have it, redraw it more neatly. Also, make a table (or include the information clearly in the diagram) regarding what information each state tells you regarding the history of the sequence you have seen thus far.
According to your state diagram, what happens should your system get 11-- as the beginning sequence? Each state should have two arrows leading from it, one for an input of 1 and another for 0. It can lead to itself, but the behavior must be defined. As WBahn noted, a state table is a nice way of encapsulating the data in your state diagram and can help your discover shortcomings in your design.