The sign of charge is an arbitrary human convention, invented before electrons were discovered. We talk of "conventional current" as flowing from positive to negative, you don't actually care whether the charge-carriers are +ve or -ve charges for circuit analysis at all.
It does matter for understanding semiconductors and electron tubes however.
In most situations we don't worry about the direction of the current anyway because it will be going one way only, we only care about how much.
Yes, we are dealing with DC here, logic circuits run off a 5V or 3.3V (or sometimes less) DC supply.