Counters Prepared by: Careene McCallum-Rodney

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.

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).

Up Counter (0 – 7)

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

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.

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

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

Up Counter (0 – 7) Timing diagram

Up Counter (0 – 7) State Table Clk Q 0 Q 1 Q 2 Value in Decimal

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

Down Counter (7 – 0)

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

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.

Down Counter (7 – 0) Timing Diagram

Down Counter (7 – 0) STATE TABLE Clk Q 0 Q 1 Q 2 Value in Decimal

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