Think of emotion as predicting future positive or negative rewards. The value of a state (or action) is related to the anticipation of reward. The fundamental role of emotion is to select actions. Rewards types are basically hard wired by evolution into our brains and are related to safety, food, companionship, learning, creativity, curiosity and a few more. They simply identify specific situations and send reward signals to the part of the brain that learns to predict future rewards.

> It doesn't look like digital computation (not digital encoding) can produce such outcomes.

We have built such systems and they work with enough training, but their training must be as agents in an environment, not as a model training on a static dataset - think AlphaGo. I think AlphaGo has learned emotion related to the world of Go (in this case emotion is related to good-move, bad move, safety and danger), and its human opponents had a lot to say about how it felt to play against it.

Emotion is not something beyond AI agents. It's just how they plan their actions. They might not be human emotions but they are emotions related to their own activity and goals.