Service manual

STP 11-25R13-SM-TG
Q - 6
constants, the variables in the theorems of Boolean algebra can only assume a 1 or a 0. Table Q-6 lists
the 13 basic theorems.
Table Q-6. Thirteen Basic Theorems
h. In
Boolean algebra, like any other type of mathematics, there are certain laws of manipulation that must be
followed. These can be proven by the use of truth tables and/or waveforms. The following is a list of
some of these basic laws.
(1) The Law of Identity
: Any letter, number, or expression is equal to itself.
_ _
A = A and A = A
(2) The Commutative Law
:
(a) When inputs to a logic symbol are ANDed, the order in which they are written does not affect
the binary value of the output.
AB = BA
(b) When inputs to a logic symbol are ORed, the order in which they are written does not affect the
binary value of the output.
A + B = B + A
T-1 A AND 0 = 0
T-2 0 AND A = 0
T-3 A AND 1 = A
T-4 1 AND A = A
T-5 A AND A = A
_
T-6 A AND A = 0
T-7 A OR 0 = A
T-8 0 OR A = A
T-9 A OR 1 = 1
T-10 1 OR A = 1
_
T-11 A OR A = A
T-12 A OR A = 1
T-13 A = A