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A typical analog circuit will use a voltage level to represent information. For example, imagine a circuit that represents numbers with voltages (an example might be the fuel gauge in a car where a certain voltage represents a certain level of fuel). In this case, let's say that 1 volt represents the number 10 and 2 volts represents the number 20, etc. With this system, 0.7 volts would represent the number 7 and 1.5 volts would represent the number 15.

The first problem is that electronic devices are not precise. Creating exactly 1.5 volts will be difficult. The next problem is that the impedance between two circuits (output and input impedances) is not precise. If one circuit tries to send exactly 1.5 volts to another circuit, there is sure to be some drop in voltage by the time the signal arrives at the second circuit. For example, 1.5 volts may become 1.47 volts. This signal degrades further as it passes from circuit to circuit. It is impossible to predict what the outcome will be.

Another problem with analog circuits is noise (any unwanted outside influence on the signal). Electromagnetic and electrostatic fields will interact with the signal. The longer the distance between circuits, the more noise that will be picked up. It the above example, noise may change the voltage. This adds another level of unpredictability. With audio circuits, noise may be manifested by unwanted sounds such as hum, buzz, clicks, pops, hiss.

A
digital circuit will use only two voltages to carry information^{[1]}.
At first observation is may seem that a digital circuit would only be able to
convey two conditions. For example, a simple switch may convey whether a fuel
tank is full or empty, but not anything in-between.

Off = Empty On = Full |

However, as with the Roman signaling, several bits of information can be used together to convey more information. How about two switches representing four states as follows.

Off Off = Empty Off On = 1/3 Full On Off = 2/3 Full On On = Full |

With three switches we can represent eight states.

Off Off Off = Empty Off Off On = 1/7 Full Off On Off = 2/7 Full Off On On = 3/7 Full On Off Off = 4/7 Full On Off On = 5/7 Full On On Off = 6/7 Full On On On = Full |

If we add more switches, which adds more bits of information, we can have finer gradations of information. This system may seem much more cumbersome than the analog system, and it is, but it has a major advantage. No switch that is off is likely to be mistaken for a switch that is on and vice versa. There is practically no chance that a 1/7-full tank, represented by Off Off On, would be mistaken for a 2/7-full tank, which is represented by Off On Off.

You may have noticed that there is no state of switches to represent half full. That's one of the disadvantages of a digital system. It can only represent discreet jumps in the levels. In the specific case in this example, none of those steps is at the half-full mark. To make those jumps smaller we have to add more bits. For example, if we use six switches, we can represent 64 levels. This is probably more than enough for the fuel level in a fuel tank. If we need smaller jumps, we can add more bits. Each time we add a bit we double the number of steps that can be represented.

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