Let L3 consist of strings in which there are never two consecutive
0s and there are never two consecutive 1s.<p>

There is a DFA that recongizes L3.  I'll describe it below.
You may want to draw it graphically.<p>

There will be 4 states.  S (representing no 0s or 1s yet),
S0 (reprenting 0 was last)
S1 (reprenting 1 was last)
Sno (representing 2 consecutive 0s or 2 consecutive 1s having occured).

The start state is S and the accepting states are S, S0, S1.<p>

Here is a table showing the transitions:
<pre>

State input   | go to state
--------------|------------
S       0     |   S0
S       1     |   S1
S0      0     |   Sno
S0      1     |   S1
S1      0     |   S0
S1      1     |   Sno
Sno     0     |   Sno
Sno     1     |   Sno
</pre>