Explanation requires ground truth: to verify an account of a system we must know its inner functioning-just what is missing where explainable AI (XAI) is most needed. Systems we can study fall into two camps. Simple, procedural one-decision trees, rule lists, sparse linear models-have a known but trivial mechanism, so explaining them tests nothing; genuinely complex ones-deep networks, real-world tasks-need XAI but have no ground-truth inner functioning, so an explanation can be plausible, confident, and wrong with no way to tell. We remove this dichotomy with a study object both genuinely complex and fully specified-inspectable by construction-and, so gradient methods apply, fully differentiable. We reimplement the Atari 2600 Video Computer System (VCS)-a real computer architecture, and the cradle of deep reinforcement learning-as two independent end-to-end differentiable emulators in Julia (jutari) and JAX (jaxtari), each validated bit-for-bit against xitari. Both reproduce xitari on all 64 supported Arcade Learning Environment (ALE) games: 64/64 byte-identical RAM and 64/64 pixel-identical screens. Treating the cartridge ROM as a weight tensor, RAM as a soft tape, and control flow as gates, we prove the differentiable (soft) execution equals the original (hard) one bit-for-bit in the forward pass at any finite temperature, while exposing surrogate gradients where the bit logic has none. The JAX port also opens a GPU path: batched differentiable rollouts reach millions of environment-steps/s on one commodity GPU. The system was built in roughly 137 active hours over 29 calendar days, much of it written autonomously by coding agents. This paper builds and validates the foundation, showing-theoretically and in a qualitative gradient study-that gradient-based XAI on it is feasible. Both ports' full code is available under the MIT license at https://github.com/akmaier/UnderstandingVCS.

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