2 counters & 3 multiplexers, nested selection based on count states, repeats every 14 elements with constant 4 prepended.
System Design:
This sequence can be implemented using two modulo-16 counters and three multiplexers:
Counters:
1. Main Counter: Counts from 0 to 15 with a clock. Outputs (A3, A2, A1, A0).
2. Step Counter: Counts from 0 to 3 and resets on reaching 4. Outputs (B1, B0).
Multiplexers:
1. M1: Selects data based on Step Counter's B1 (high for Main Counter A3, low for constant 7).
2. M2: Selects data based on Step Counter's B0 (high for M1 output, low for Main Counter A2).
3. M3: Selects data based on combined output of M2 and Main Counter A1 and A0 (high for M2 output, low for constant 4).
Output:
The final output is the selected data from M3.
Clocking:
Main Counter: Continuously clocks.
Step Counter: Clocks only when Main Counter reaches 0.
Sequence Explanation:
Initially, M1 outputs A3 (7) because B1 is high.
M2 and M3 outputs depend on A2 and A1, generating the first eight elements.
When the Main Counter reaches 0, the Step Counter increments, triggering its reset.
This resets M2 and M3's selection to default, repeating the first eight elements with a constant 4 prepended.