Logic Diagrams
DOE-HDBK-1016/2-93
TRUTH TABLES AND EXERCISES
Rev. 0
Page 11
PR-05
TRUTH TABLES AND EXERCISES
Truth tables offer a simple and easy to understand tool that can be used to
determine the output of any logic gate or circuit for all input combinations.
EO 1.3
DEVELOP the truth tables for the following logic gates:
a.
AND gate
d.
NAND gate
b.
OR gate
e.
NOR gate
c.
NOT gate
f.
EXCLUSIVE OR gate
EO 1.4
IDENTIFY the symbols used to denote a logical 1 (or high)
and a logical 0 (or low) as used in logic diagrams.
EO 1.5
Given a logic diagram and appropriate information,
DETERMINE the output of each component and the logic
circuit.
Truth Tables
When a logic gate has only two inputs, or the logic circuit to be analyzed has only one or two
gates, it is fairly easy to remember how a specific gate responds and determine the output of
the gate or circuit. But as the number of inputs and/or the complexity of the circuit grows, it
becomes more difficult to determine the output of the gate or circuit. Truth tables, as illustrated
in Figure 11, are tools designed to help solve this problem. A truth table has a column for the
input of each gate and column for the output of each gate. The number of rows needed is based
on the number of inputs, so that every combination of input signal is listed (mathematically the
number of rows is 2 , where n = number of inputs). In truth tables, the on and off status of the
n
inputs and outputs is represented using 0s and 1s. As previously stated 0 = off and 1 = on.
Figure 11 lists truth tables for the seven basic logic gates. Compare each gate's truth table with
its definition given earlier in this module, and verify for yourself that they are stating the same
thing.
