Asynchronous Counter: Use cascaded flip-flops to create binary counting sequences.
Up/Down Counter: Digital circuit that can increment up (count up) or down (count down) depending on the control inputs.
- Since it isn’t controlled by a clock signal, it is asynchronous.
Example: 1, 2, and 3-bit up counter 
- Clock
- One bit Up Counter
- Two bit Up Counter
Example: 3-bit Up Counter Circuit
Output:
q0: 0 1 0 1 0 1
q1: 0 0 1 1 0 0
a2: 0 0 0 0 1 1
Or, looked at vertically, we can see how it counts up
| Step | q1 | q2 | q3 | Numeric |
|---|
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 2 |
| 3 | 0 | 1 | 1 | 3 |
| 4 | 1 | 0 | 0 | 4 |
| 5 | 1 | 0 | 1 | 5 |
Example: 3-bit Down Counter Circuit
- This is the same design at the Up Counter, we just look at Q’ instead of Q.
Example: Up/Down Counter Part 
Example: Frequency Division 
- This divides the frequency by 2.
- Chain to divide by powers of 2. (2, 4, 8, …)
- This is the same behavior as the counter, except we only observe the final output
- Up or down counter doesn’t matter for frequency division because we only look at the final Q in the chain.
Example: Frequency Multiplication 
- This multiplies the frequency by 2.
- Chain to multiply by powers of 2. (2, 4, 8, …)
- Don’t look at this as logic, look at this as frequencies.
- The buffer functions as a delay
- The delay doesn’t need to be super precise, though it’ll affect the duration of how long it stays at high and low frequencies.