Ben Eater's breadboard CPU is a good way to learn the basics, but since the focus is pedagogical, it's very underpowered for the quantity of chips it uses (and you better enjoy forming wires). For a much more powerful computer built around the same number of TTL chips, see the Gigatron.

RE .... See the Gigatron. Google link https://www.google.com/search?q=Gigatron+CPU&oq=Gigatron+CPU gives lots of good explanatory links . (I had never heard of it , it looks quite interesting .... )

And no microprocessor!

But as I understand it the kits are no longer available :-(