The circle is always a part of a symbol. It is never used
alone on a line to indicate signal levels or any other fact.
c. The state indicator allow us to predetermine the input signals required for any circuit and the
circuit's output level without regard to the function of the circuit. This fact will be correct regardless of
the symbol. As we discuss each symbol, we will use the shape of the symbol to determine its circuit
function, and the state indicators (circles) to determine the inputs required and the output produced.
Figure 1-3. An inverter symbol
When a binary circuit produces an output that is exactly the opposite of the input, it is called an
inverter. The symbol for an inverter is shown in Figure 1-3. The inverter symbol is the only symbol
that will have one input and one output. All others will have two inputs or more. The inverter is
considered a NOT gate.
The state indicator (circle) is shown as part of the inverter symbol on either its input or its output.
It depends on whether the output is considered active when it is high or when it is low. Both versions of
the symbol indicate that when the input is high the output is low and when the input is low the output is
high. A comparison of the truth tables in Figure 1-3 proves this to be true.
An inverter performs the function of negation on signals and negates the Boolean expression of
the input signals. Boolean algebra is a system of mathematical logic, using the function AND, NOT,
and OR. In the Boolean system, AND is represented by multiplication, NOT by complementation, and
OR by addition. So X and Y is written XY or X Y, NOT X is written X', and X OR Y is written X +
Y. Boolean functions are used in the design of digital logic circuits. A simple term such as B at the
input to an inverter becomes B at the output. An expression such as A + B becomes A + B after an
inverter. Simplifying this expression, (A + B) = (AB), we find that A + B becomes AB when it is
inverted. This shows that an inverter negates the function, as well as the signal conditions in an