Exercise 3: Why a Feedback Circuit Isn't Combinational — Possible Solution ==================================================================== THIS CHAPTER'S OWN DEFINITION ------------------------------ A combinational circuit's output depends ONLY on its current inputs - never on anything that happened before. THE PROPOSED CIRCUIT ------------------------------ output = A AND (output from one clock cycle ago) APPLYING THE DEFINITION DIRECTLY ------------------------------ This circuit's own output does not depend only on its current inputs (A, in this case) - it also depends explicitly on its own PAST output, from one clock cycle earlier. That earlier output is not a current input at all; it's a stored result the circuit is reaching back into its own history to reuse. This directly violates this chapter's own definition: the current output is a function of (current input A) AND (something that happened in the past), not a function of current inputs alone. WHY THE COMPONENTS USED DON'T MATTER HERE ------------------------------ The fact that the circuit is built entirely from an AND gate - a perfectly ordinary combinational gate on its own - doesn't make the overall circuit combinational. What determines combinational- vs-not isn't which gate types are used, it's whether the circuit's own output ever depends on anything besides its present inputs. Feeding a circuit's own past output back into itself introduces exactly the kind of dependency on history that disqualifies it, regardless of how simple or ordinary the gate computing the combination is. RESULT ------------------------------ This circuit is NOT combinational, because its output genuinely depends on more than just its current inputs - it depends on its own stored past output too. This is, in fact, exactly the structure Chapter 8's own sequential logic is built from - a circuit that remembers something is precisely what "feeding output back as an input" produces. WHY THIS WORKS AS AN ANSWER ------------------------------ The definition is applied literally and directly to the specific circuit described (checking whether the output depends on something beyond current inputs), rather than reasoning from "AND gates are combinational, so anything built from them must be" - which is exactly the tempting but incorrect shortcut this exercise is designed to catch.