[Animats]

I once took a computer architecture course from the designer of the Burroughs 6700, who had us do a similar exercise. But that was back when people actually built things out of 74xx TTL. Few people do that any more. It would be very unusual to use a 4-bit adder chip today, unless you're deliberately doing retro stuff. And even more unusual to start there. Also, a 4-bit adder, a stateless device, is only useful when surrounded by latches and clocks so that something useful happens.

Here's a real beginner level presentation, from Adafruit.[1] This may be too simplified for some.

The Art of Electronics by Horowitz and Hill is highly recommended, but the original audience was physics grad students who needed to build instrumentation for physics experiments. The order of presentation is good, but it's a big book. Because it mentions current components by part number, the book ages rapidly.

[1] https://learn.adafruit.com/guides/beginner