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Digital circuits
Ultimately every process in a computer is the product of a digital circuit that is working on binary values. In contrast to electrical circuits, digital circuits are not represented in an analogue fashion.
Analogue circuits work on the basis of real continuous phenomena in the world: charges and currents. As a result, the key properties of a circuit - voltage, current and resistance - can vary over a wide range of values. This is the reason that we require components like batteries and resistors: to control the natural flow of current and ensure that it only runs within desired parameters.
In a standard electrical circuit, voltage, current and resistance can vary over a wide range of values however in the binary context we want to deal with discrete values (zeros and ones) which can be fed into the various logic gates.
We therefore need a way to represent 'on' and 'off' as single quantities. We do this by stipulating that a given voltage corresponds to 'on' (high) and another corresponds to 'off' (low). Of course these are not really discrete values since voltage is inherently analogue but we basically binary-encode them. Formally 'on' has a voltage of 1 and 'off' has a voltage of 0. In reality 'on' tends to be within 2-5V depending on the circuit design and anything between 0 - 0.8V is considered off.
The transistor is the electrical component that enables us to represent given voltage ranges as being 'on' or 'off'.