Counters

Complete a timing diagram for this synchronous counter circuit, and identify the direction of its binary count:

Synchronous counter circuits tend to confuse students. The circuit shown here is the design that most students think ought to work, but actually doesn’t:

Shown here is an up/down synchronous counter design that does work:

Explain why this circuit is able to function properly (counting in either direction), while the first circuit is not able to count properly at all. What do those “extra” gates do to make the counter circuit function as it should. Hint: to more easily compare the up/down counter to the faulty up counter initially shown, connect the Up/[Down] control line high, and then disregard any lines and gates that become disabled as a result.

The following circuit is a two-bit synchronous binary up/down counter:

Explain what would happen if the upper AND gate’s output were to become “stuck” in the high state regardless of its input conditions. What effect would this kind of failure have on the counter’s operation?