1. Basic Counters: Part I Section 7-6 (pp. 353-366)

2. 2 Definition Counter is a register that goes through a sequence of states as it is clocked Binary counter ♦ Counts through a binary sequence Example: 2 bit “up” counter; a circuit with 2 FFs that goes through the sequence of states: (00, 01, 10, 11) 2 = (0, 1, 2, 3) 10 ♦ n bit “up” counter counts from 0 to 2 n – 1 ♦ n bit “down” counter counts from 2 n – 1 to 0

3. 3 Waveforms of a 2 bit Counter Counter CP B A 0123 01

4. 4 Ripple Counter Simple So Q will alternate H and L Why called ripple counter?

5. 5 Synchronous Counters Clock inputs of all FFs receive a common clock pulse Change in state is determined from the present state of the counter

6. 6 Synchronous Counter Count enable, EN = 0 ♦ counter remains in the same state Count enable, EN = 1 ♦ counter counts up Carry output, CO used to expand counter (e.g. to 8 bits)

7. 7 Arbitrary Count Counter goes through an arbitrary sequence Example: States 3 and 7 are not used

8. 8 State Diagram of Example Arbitrary Counter Analysis of state diagram shows: if circuit ever goes in an unused sate (011 or 111) the next clock transfers it to a valid state

9. 9 Circuit of Example Arbitrary Counter