By "with some care", I meant of course "if you know what you're doing"

To clarify: It is perfectly possible to break the rules (actually, they're more guidelines) and use unsuitable construction such as wire-wrap or point to point techniques for quite high-speed digital circuits, but you have to be aware of what is likely to break and how to fix it. Common issues are signal crosstalk, power spikes, ground bounce, signal reflections (which takes us into transmission line theory, and you don't want to go there), and voltage drops due to inductance and capacitance issues. All of these problems can be overcome, assuming you can correctly identify them and know the magic passes needed to rectify them

Doing everything on a proper PCB makes life much easier. Double-sided boards are the easiest and cheapest, but still have limitations, some of them the same as above, but will usually allow more consistent results and to higher frequencies than wire-wrapping. In addition, with a PCB you can use surface mount chips easily, whereas wire-wrapping an 80-pin quad flat pack chip is fiddly. Not impossible (you glue it down upside down and use lots of very fine wire), but fiddly.

Going to a 4 layer board allows you to run the power and ground planes completely separately from the signal layers, which makes layout easier and improves the chances of the circuit working correctly, especially at high frequencies. With a solid ground plane you can dramatically lower the track inductance, increase the current available to the circuitry thus reducing the amount of decoupling capacitance required, and shield the circuit both from transmitting and receiving RFI much more effectively. Mixing multiple different power planes in one layer, or separating analogue and digital ground planes is merely a matter of experience.

If your circuit is more complex, you can of course go to more layers. The most I have ever required is 10 (the empeg is 8), and the majority of the extra layers are signal ones rather than power layers. I know of PCB manufacturers that can go to around 24 layers, and you can even utilise buried vias (ie connect one layer to another without the connection going all. the way through the PCB as they normally do), and even buried components, although this last is incredibly expensive and very rare.

One last tip: always make your power tracks as wide as you can manage. It helps.

pca