PHYS345 Electricity and Electronics

Quiz 9: Sequential Logic

Consider this state counter constructed from D flip-flops and OR gates. The two flip-flops are clocked simultaneously with the same CLK.

2-bit state counter

Complete enough of the timing diagram below to determine the sequence of states that are accessed (allowed) by this counter. Start with all Qs=0 as shown.

Comment on excluded states (if any) and indicate the point of entry into the counting sequence on a state diagram.

Solution

The OR gate for FF1 is setting up Q'1+Q'2. The OR gate for FF2 is setting up Q1+Q'2.

From each combinations of Qs, the Ds are set up for the next transition as follows:

Timing diagram template

The state diagram for this counter is:

State diagram

The excluded state is (00); if the counter starts in that state for some reason, it will go to the state (11), otherwise (00) is never allowed. The sequence (11),(10),(01) is repeated, so I call this a 3-2-1 counter.


"http://www.physics.udel.edu/~watson/phys345/quiz/9soln.html"
Last updated Nov. 19, 1998.
Copyright George Watson, Univ. of Delaware, 1998.