A logic system is one that anything it does can be translated to a true
or false, present or absent, high or low, in other words, two opposite
and contrasting states where the system can only be at one of them at
any one time. Digital electronics use only two voltage levels to work
with, one to represent a true, 1 or high (usually 3v or 5v) and another
to represent false, 0 or low (a connection to ground, which is at 0v),
which make the basis of any logic system.
But what does a true represent in a logic circuit? anything you can
think of, it depends on what you are using it to model. One of the most
used introductory digital systems is that of a car key alarm, where if
the door is open while the key is still in the ignition, a buzzer alarm
will sound alerting you not to let the key inside the car when you close
it.
To construct a digital circuit for this alarm, you use one input to
represent whether the door is open (will be true when it is open, false
when closed) and another to represent whether the key is in the ignition
(will be true when in the ignition, false when not). For this circuit
we want the buzzer to sound when both conditions are true: the door is
open and the key is in the ignition.
A digital system is not concerned if the key is only half in, at the on
or off position or if the car is only half open or it didn't close
correctly; all of these situations are either forced to one state of the
other, or switching between both at a very high rate, but it must have
one of only two values.
As you can see, we have modeled a fairly complex situation (an alarm
controlled by a door and a key) to only two inputs that take only two
values. This is what makes digital circuits very useful, they are
dependable (a half closed door is an open door, just as a slightly open
door).
