Sequential logic (AQA A-Level Physics): Revision Notes

13.5.2 Sequential logic

Key Components of Sequential Logic

Binary Counters:

• Binary Counters are circuits that count pulses in binary, typically controlled by a clock signal. A basic 4-bit binary counter has the following inputs and outputs:
  • CK (Clock Input): This is where the clock pulses enter the circuit. Each pulse increments the counter.
  • U/D (Up/Down Control): Determines counting direction. If the signal is 1, the counter counts up; if it's 0, it counts down.
  • MR (Master Reset): Resets all counter outputs to 0 when triggered by a signal of 1.
  • Outputs (Q₀ to Q₃): The counter's binary output, where Q₀ is the Least Significant Bit (LSB) and Q₃ is the Most Significant Bit (MSB).

Counter Operation and Timing:

• Each output in the counter changes state based on clock pulses, with Q₀ changing every pulse, Q₁ every second pulse, and so on, making Q₃ the slowest-changing bit. This characteristic allows the counter to act as a frequency divider.
• A timing diagram visualises the behaviour of each bit (Q₀ to Q₃) in response to clock pulses, showing how binary values increase or decrease over time.

Counting Cycle and Resetting:

• The counter continues to count up to $2^n - 1$ for an n-bit counter, resetting to zero after reaching the maximum count. For a 4-bit counter, it will count from 0 to 15 (binary 0000 to 1111) and then reset.

Modulo Counters:

• Modulo-N Counters reset at any chosen number, not just powers of two. For instance, a modulo-10 counter (also known as a BCD counter) will reset after reaching 9. This can be achieved by connecting logic gates to control the master reset based on a desired output.
• Example: A BCD Counter (Binary-Coded Decimal Counter) resets after reaching decimal 9, making it useful in digital displays that show values from 0 to 9.

Johnson (Decade) Counter:

• A Johnson Counter (or Decade Counter) cycles through a sequence of 10 states, with outputs turning on and off in sequence. Unlike binary counters, its outputs do not represent binary values but rather a sequence pattern. This type of counter has applications in timing circuits.
• The timing diagram for a Johnson counter shows the unique sequence of states over several clock pulses.

Sequencing Applications:

• Johnson Counters and other sequential logic counters are often used in systems that require operations in a specific order or timing, such as heating elements or motors controlled on specific time cycles.
• Example Application: A sequencing circuit might control a heating element for 3 seconds, wait 2 seconds, then activate a motor for 2 seconds in a repeating 10-second cycle.

Important Notes

• Carry Out (Cₒ): Many counters have a carry-out feature that allows the output to act as a clock signal for another counter. This lets multiple counters connect in series to count higher values.
• Rising-Edge Triggering: These counters respond to the rising edge (from 0 to 1) of the clock pulse. Sequential logic circuits are essential in applications requiring time-based operations, from digital clocks to complex programmable systems, and provide foundational understanding for more advanced digital electronics.