Sequential circuit design objective When you deliberately design the next-state logic so that the machine follows a non-natural order of states (e.g., 0 → 5 → 2 → 7 …), the sequential circuit design is used to ________.

Introduction / Context:
Finite-state machines and counters can be engineered to step through states in virtually any desired sequence. Beyond simple up/down patterns, designers often implement custom (pseudo-random or application-specific) sequences to meet timing or control requirements.

Given Data / Assumptions:

• “Random order” here means an arbitrary, pre-defined sequence, not truly random noise.
• Next-state logic can be derived to realize any permutation over the valid state set, with unused states redirected safely.
• Clocking is synchronous; transitions are governed by combinational logic feeding the state register.

Concept / Approach:
The question asks for the broad purpose of sequential design: shaping the next-state map to traverse a chosen sequence. Classical examples include Johnson counters, Gray counters, or application-specific “random-looking” sequences used in scanners, LED chasers, or test pattern generators.

Step-by-Step Solution:

Verification / Alternative check:
Simulate the state machine for several cycles; confirm it follows the custom sequence and handles illegal states with resets or self-correction.

Why Other Options Are Wrong:
“count up” and “count down” are special cases of sequential design but not the general aim stated. “decode an end count” is a separate task performed by decoders or comparators.

Common Pitfalls:
Neglecting unused states can cause lock-up. Always define recovery for illegal states and ensure synchronous reset behavior.

Final Answer:
count in a random order