Could you develop a range of counters, including a mod-15 counter that omits 0, 3, 4, 8, and 5?

Question Analysis

The question is asking you to design a series of counters, with a specific focus on creating a mod-15 counter. This counter must cycle through a sequence of numbers from 0 to 14, but it should omit the numbers 0, 3, 4, 8, and 5. This implies that your counter will have a custom sequence rather than a straightforward count from 0 to 14. To achieve this, you'll need to understand how to implement state machines in digital circuits and how to manipulate typical counting sequences to skip unwanted states.

Answer

To develop a mod-15 counter that omits 0, 3, 4, 8, and 5, follow these steps:

1. Identify Required States: First, determine the sequence of numbers you want the counter to cycle through. Since you need to omit the numbers 0, 3, 4, 8, and 5, the sequence will be: 1, 2, 6, 7, 9, 10, 11, 12, 13, 14.

2. Total States: You will have 10 states in total, one for each number in the sequence.

3. State Assignment: Assign binary values to each state. This is crucial as it will determine the logic for your counter. You can use a binary encoding that suits 10 states, which can be covered by a 4-bit binary number.

   • 0001: 1
   • 0010: 2
   • 0011: 6
   • 0100: 7
   • 0101: 9
   • 0110: 10
   • 0111: 11
   • 1000: 12
   • 1001: 13
   • 1010: 14

4. Design Logic: Use flip-flops (like JK or D flip-flops) to build the counter. The logic circuit will be built using these flip-flops to move from one state to the next.

5. Implement Transition Logic: Develop the combinational logic necessary for the transition between these states, ensuring that the omitted numbers are not part of the sequence. This involves designing the logic gates that connect the outputs of the flip-flops to their inputs for the next state.

6. Circuit Implementation: Using a hardware description language (HDL) like VHDL or Verilog can be helpful to simulate and implement the design on an FPGA or similar device.

7. Testing: Verify the counter's functionality by simulating the circuit to ensure all omitted states are correctly skipped and the sequence accurately follows the desired pattern.

This approach ensures a systematic design of a counter that achieves the specific requirements given in the question.