Shift registers used as counters — to make a shift register function as a circulating counter (e.g., ring or Johnson type), how should its connections be arranged between serial output and serial input?

Introduction / Context:
A shift register can be repurposed as a counter by recirculating data through its stages. This question asks what connection enables a shift register to generate a repeating sequence of states, as used in ring and Johnson counters for timing and sequence generation.

Given Data / Assumptions:

• A multi-bit shift register with clocked shifting.
• Desire to obtain a repetitive count/sequence of outputs.
• Proper initial seeding (e.g., one-hot or suitable pattern) is available.

Concept / Approach:
In a ring counter, a single 1 shifts through the register stages. In a Johnson (twisted-ring) counter, the inverted serial output is fed back to the serial input to create a 2N-state sequence for an N-bit register. In both cases, the essential idea is feedback from the output end of the shift register back to its input, which circulates a pattern deterministically with each clock pulse.

Step-by-Step Solution:

Verification / Alternative check:
Examine the state diagram: with feedback, the register cycles through a fixed sequence length (N for ring, 2N for Johnson) before returning to the seed, which is the hallmark of a counter-like behavior.

Why Other Options Are Wrong:

• Use serial in as counter input and serial out as output: Without feedback, no closed cycle is produced.
• Parallel inputs as clocked sources with serial output: Misuses the parallel load function; does not create a cyclic sequence.
• Only SISO without feedback: A SISO shifts data out and loses it; no counting loop forms.

Common Pitfalls:
Forgetting to seed the register (all-zeros ring locks up), or omitting the inversion required for Johnson counters. Also, confusing shift-direction conventions can flip left/right notions but the feedback principle remains the same.

Final Answer:
Connect the serial output back to the serial input (with proper seeding/inversion as required).