When he was a toddler, the age of your child, he used to practice things. That wasn't anything to make anyone think he was gifted, it was just... his temperament. I remember him imitating the radio when he was trying to learn to speak, saying harder words to himself. Kids around that age sometimes develop little obsessions, like with dinosaurs or cars. My kid liked penguins and he learned everything he could about them.
As he became more verbal, he began integrating every new bit of information into his play. He still does this at 10, wandering around the house muttering under his breath, creating little science fiction stories that are a stew of science facts and daydreaming and other bits and pieces. Or he'll actually include me, telling me about a superhero he's creating, and the story integrates all kinds of stuff he's picked up here and there--apparently brain science is interesting to him. (He also went through a preschool phase of making me do arithmetic because HE found it calming. Um. I didn't.)
As far as letters and numbers--he was fascinated by letters, but not an early reader. He used to make drawings in preschool that were maps, featuring letters and numbers as decoration, a sort of kabbalistic sense of them as characters. As an older child he was fascinated by secret codes. Every so often I find a notebook from earlier than I remember the code thing starting, with the beginnings of a code in it.
This, right here, is my favorite part of being a mom.