1. Counters Prepared by: Careene McCallum-Rodney

2. Introduction Counters uses a Toggle Flip Flops to count either UP or DOWN in binary. A toggle flip flop is needed for each bit in the number.

3. Introduction If you are counting from 0—7, you will need 3 bits (because the largest number can be represented using 3 bits). If you are counting from 0—15, you will need 4 bits (because the largest number can be represented using 4 bits).

4. Up Counter (0 – 7)

5. Activity 1 Draw the block diagram for the up- counter from 0 – 15, inclusive.

6. Up Counter (0 – 7) The up counter connects the 2nd and 3rd TFF to the Q output. ◦ What this signifies is that the same way Q started that’s how the other two TFFs will start.

7. Up Counter (0 – 7) The first TFF will toggle every 2 clock periods. ◦ A clock period is each time the clock changes its state (i.e. the clock being on 0, 1, 0, 1 is 4 clock periods). 2 clock periods

8. Up Counter (0 – 7) The second TFF will toggle every 4 clock periods. The third TFF will toggle every 8 clock periods. 2 clock periods 4 clock periods 8 clock periods

9. Up Counter (0 – 7) Timing diagram

10. Up Counter (0 – 7) State Table Clk Q 0 Q 1 Q 2 Value in Decimal 1 0000 10011 1 0102 10113 11004 11015 11106 11117

11. Activity 2 Draw the timing diagram for the up- counter from 0 – 11, inclusive.

12. Down Counter (7 – 0)

13. Activity 3 Draw the block diagram for the down- counter from 15 - 0, inclusive.

14. Down Counter (7 – 0) The down counter connects the 2nd and 3rd TFF to the Q’ output. What this signifies is that the same way Q’ started that’s how the other two TFFs will start.

15. Down Counter (7 – 0) Timing Diagram

16. Down Counter (7 – 0) STATE TABLE Clk Q 0 Q 1 Q 2 Value in Decimal 1 1117 10116 1 1015 11004 10113 10102 10011 10000

17. Activity 4 Draw the timing diagram for the down- counter from 15 – 5, inclusive.