This project is about how to build an 8 bit computer on breadboards, from 7400 series basic TTL. I am currently in the process of building mine, and will give an overview of what's involved. It is a great project that can teach you a lot about how a computer works at a basic level, and it allows for adaptations and expansion to your own interest. The computer will be able to perform basic programs such as computing the Fibonacci sequence.
There are many resources out there that teach you how to build a computer. Ben Eater’s Youtube video series and the Digital computer electronics book by Albert Malvino are the perfect guides on how to do this. People have also built their own variants and written about them online.
Ben Eater's completed computer (amazing wiring!!). Source: i.ytimg.com/vi/35zLnS3fXeA/maxresdefault.jpg
You will need breadboards, many different TTL chips, LEDs and some 20-24 gauge solid copper wire. I’d recommend making solid connections, particularly with the power rails, as the breadboards can have high resistance and a large voltage drop if there isn't enough wire or good enough connections.
Pictured below is my completed A register, B register and arithmetic logic unit (I trust your wiring will be many times neater than mine!). These modules interface with the bus and its data, then perform either addition or subtraction on that data, and output again to the bus. The LEDs show the contents of these registers. The registers use 2x 4 bit D-type registers - 74LS173s, and an octal tri-state buffer, the 74LS245.
I've also built the computer's clock, to coordinate the operations. It utilises 555 timers and some logic to provide either a constant signal at variable speed or a manual pulse from a debounced switch. The speed control is to either run the computer fast to achieve the result best or to slow it down and actually see the operations happening. The manual switch is great to advance the program one step at a time to troubleshoot or check things.
Next I will be building the memory module for data and programs, the memory address system, and the programming circuitry for the computer. After that, the instruction register, program counter, control logic and output register. The output register uses the same D-type registers as in the rest of the computer, EEPROM or RAM chips, binary-decimal converters and 7 segment LED displays. In my computer I hope to also use some graphics processing and maybe an Arduino to output to a LED matrix. The computer could then output animations and patterns to the matrix.
Use the spare power rails to make the computer's central bus.
The great thing about this computer is not only its computing but also the learning that comes with building it and the capacity to modify it like I plan to do. You can bring your own ideas to the design and expand how you like. I definitely recommend that you go and learn more, perhaps even have a go!