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Digital circuits work on the basis of a transistor being used as a switch.
Consider a light switch, a transistor can be considered almost the same and in some circuits transistors are used to control large amounts of power with very little input power being used. Look at figure 1 below. Here are two crude transistor switch circuits. This load could also be replaced by a small light bulb, relay or LED in conjunction with a resistor of suitable value. In any event the bulb or led would light or the relay would close.