You want to build a CPU using logic gates?? Back to the 1970s! That’s a tall order, considering that even the earliest humble microprocessors had thousands of logic gates and now have millions. You’ll need to construct registers, latches, flip-flops, half-adders, full-adders, status flags, and all manner of clever intermediate structures—a densely populated circuit board just to emulate the humblest 8-pin CPU. Not that it isn’t a worthy project…
Might I suggest you focus on interfacing something like an Arduino, Propeller, or even a raw PIC chip (in other words, a modern embedded controller) as the centerpiece of your computer, then branch outward with simple digital logic from there for the peripherals? You can still assemble TTL chips like so many Legos to form useful circuits. (Been there, done that!)
Or perhaps just build yourself a one- or two-bit processor, implementing all the basic logic functions (not, and, or, add, etc) once or twice—but not 8-fold or 16-fold or more like a real CPU. Forget about multiplication—the earliest commercial chips lacked this function as it is readily handled in software. I’ve hand-written my own floating point multiply, divide, and binary-to-decimal conversion, almost 30 years ago. Once again not for the faint of heart & I wouldn’t do it again.
You’ll also need to construct a digital oscillator to serve as a clock, plus tons of logic to drive the whole fetch-and-process cycle of digesting your software byte by byte.
Back in the day, I learned from books that are now probably out of print. Look for early stuff by Don Lancaster (aka “hardware hacker”) such as TTL Cookbook and CMOS Cookbook. Other authors to search for are Osbourne and Selby. Sorry I have no up-to-date references.
I admire your ambition! Like building an aircraft carrier from toothpicks.