Designing a divide-by-200 modulus counter using synchronous building blocks “Two 4-bit synchronous counters can be cascaded to make an 8-bit counter as a basis for a divide-by-200 design.” Evaluate this design statement.

Introduction / Context:Divide-by-N counters are widely implemented using standard 4-bit synchronous counter ICs (or HDL modules) cascaded to expand the count range, then modified to reset at the desired terminal count. This question checks whether two 4-bit counters can serve as the foundation for a divide-by-200 solution.

Given Data / Assumptions:

• Two 4-bit synchronous counters, when cascaded, form an 8-bit synchronous counter.
• An 8-bit counter provides a range of 0–255 (256 states).
• Divide-by-200 means the output period should be 200 input clock cycles.

Concept / Approach:The approach is to use the 8-bit count to detect a terminal count (199 or 200, depending on design convention) and synchronously clear (or preset) back to zero. By decoding the desired count and feeding a synchronous reset, the sequence length becomes exactly 200, achieving a ÷200 ratio.

Step-by-Step Solution:Cascade two 4-bit synchronous counters to obtain 8 bits: count range 0–255.Choose terminal count: typically reset when the count reaches 199 so the sequence length is 200 states (0 through 199).Design decode logic to assert a synchronous reset at count = 199 (1100 0111 for 199 decimal), or preset at an offset if preferred.Verify that all flip-flops share the same clock so reset occurs cleanly on the next edge.

Verification / Alternative check:Simulation with a testbench counting cycles confirms that the output toggles or a pulse is produced every 200 clocks. Hardware implementations using common 74HC/SN74 synchronous counter families follow the same principle.

Why Other Options Are Wrong:“Incorrect” ignores the standard modulus reduction technique. “Only correct for ripple counters” is backwards; synchronous counters are preferred. “Only correct if using gray-code counters” is unnecessary; binary counters suffice.

Common Pitfalls:Using asynchronous clear mid-cycle causing glitches; decoding the wrong terminal count; not meeting setup/hold for the synchronous reset path.

Final Answer:Correct