If a modern computer that would not work because you control the metal–oxide–semiconductor field-effect transistor (MOSFET) with the gate voltage.
What you control is the current flow between the source and drain with the gate voltage. So you have a voltage controlled current switch. In a ideal transistor there no current flow from the gate to the source or drain.
Electronically the gate is like a capacitors connected between it and the drain and source. The voltage it has will depend on the number of extra electrons it have in it. You could look at it as charge control but that make it harder since the capacitance of the gate, the wires through differs between different transistors.
Because voltage, current and other electrical parameters of the system in interconnected you could think of it as control by the amount of charge at the transistor gate but that make it a lot more complicated model.
What you do in digital logic is to have the gate at 0 V or at the supply voltages so the current through the transistor is zero or maximum. The max current will charge up the capacitor in the wires and gates of other transistors and increase the voltage to control the. You do the same with transistors connected to the ground but then you drain the electrical charge.
In older bipolar junction transistor (BJT) the current into the base control the current flow between the collector and emitter. For them looking at is as current controls make more sense but they are not used for CPUS today as it would use a lot more power.
If FLASH memory the data is stored as a electrical charge in a floating-gate MOSFET. So data is stored as trapped charge that result in a voltage. So you can say that data is stored as electrical charge but at the same time they produce a voltages because of the interconnection.
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