Could I accomplish the same thing as the CD4093 IC if I used 4 single NAND
gates? In other words, if this chip is just 4 NAND gates, why does it need
to be connected to power and ground?
A 4093 has schmitt trigger inputs, which makes it different from an average
nand gate. If it's specified, or there is a need for a schmitt trigger
input, then the results will suffer or not work at all if you use something
without schmitt trigger inputs.
You also will have a hard time finding single nand gates. Oh, I gather
there may be some, but generally you'll need more than one so it makes
little sense to only put one in a package, the cost of adding the other
three will likely be less than the cost of the packaging.
I don't know where you're going with the power bit. Any gate will need
power.
Michael