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Check out Xilinx's microcontrollers picoBlaze that use a small amount of CPDL gates. Ok it is 8 bits, but that is handy for a reasonable amount of address space. 8 bits it more useful because it takes two 8 bit additions for a 16 bit total addressing calculations using central 8-bit ALU. 4-bit ALU would need 3-4 chained additions to make useful address space.
That video teaches you some good fundamentals, but it would be a long job to build that circuit just to prove what it teaches.
There are software simulation programs that could easily do the same as any hardware.
You can also follow on those basic functions by many of the online tutorials / ytubes.
Your reference to a digital computer could be interpreted in many ways.
You might find some retro sites on building old ic type computers like Z80s, but the cost and physical complexitiy of building one from transistors or basic logic gates simply is not practicable.
Rather than trying to recreate 50 year old machines why not learn some of todays simpler micros like the Pic 16F range which you can equally use to demonstate everything from simple logic functions to complex operations, by utilising both hardware and software examples.