20 4 pin power supply 24 pin motherboard

The cable adapters are useless. The 4 extra wires will not help the PSU provide more current than with the 20 pin cable.

And there's a very good chance that your old power supply will not work. The old PSU's are designed with relatively heavy heavy 3.3 and 5 volt rails and a relatively light 12 volt rail. This is just the opposite of what a modern PC needs.

Yep, re-reading that article made me remember the warnings;
"... you can plug a 20 pin cable into a 24 pin motherboard and it will work just fine. At least, it will for a while. They added those extra 4 pins for a reason. When you plug a 20 pin cable into a 24 pin connector you're not providing the extra current carrying capacity which may be needed by the motherboard. If your motherboard's current requirements are low enough then it will work properly with only a 20 pin power cabled plugged in. But if the motherboard draws enough current, then you can overheat the 20 pins you're using on the 24 pin connector. I've seen enough pictures of burned ATX main connectors to assure you that this happens. In adding the extra four pins, 3.3 volts went from 3 to 4 lines. 5 volts when from 4 to 5 lines. 12 volts went from 1 to 2 lines so its capacity doubled. Connectors really do get hot if you overload them so the safest thing to do is use a real 24 pin power supply on a motherboard with a 24 pin connector."
Same with the 4 instead of 8 pin cpu power