Page 55 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Primitive Logic Functions

Consider an electrical circuit consisting of a power supply, a light, and two
switches connected in series (one after the other). The switches are the inputs
to the circuit and the light is the output. A truth table provides a convenient
way to represent the operation of the circuit (Figure 5-1).
As the light is only ON when both the a and b switches are CLOSED (ON),
this circuit could be said to perform a 2-input AND functi0n.l In fact, the
results depend on the way in which the switches are connected; consider
another circuit in which two switches are connected in parallel (side by side)
(Figure 5-2).
In this case, as the light is ON when either a or b are CLOSED (ON), this
circuit could be said to provide a 2-input OR function.2 In a limited respect, we
might consider that these circuits are making simple logical decisions; two
switches offer four combinations of OPEN (OFF) and CLO5ED (ON), but only
certain combinations cause the light to be turned ON.
Logic functions such as AND and OR are generic concepts that can be
implemented in a variety of ways, including switches as illustrated above,
transistors for use in computers, and even pneumatic devices for use in hostile
environments such as steel works or nuclear reactors. Thus, instead of drawing
circuits using light switches, it is preferable to make use of more abstract forms
of representation. This permits designers to specify the function of systems with
minimal consideration as to their final physical realization. To facilitate this,
special symbols are employed to represent logic functions, and truth table
assignments are specified using the abstract terms FAL5E and TRUE. This is
because assignments such as OPEN, CLO5ED, ON, and OFF may imply a particu-
lar implementation.

1 A 3-input version could be constructed by adding a third switch in series with the first two.
2 A 3-input version could be constructed by adding a third switch in parallel with the first two.