Service manual

STP 11-25R13-SM-TG
Q - 7
(3) The Associative Law
: It makes no difference in what order parts of an AND or an OR
expression are combined:
A(BC) = ABC
A + (B + C) = A + B + C
(4) The Idempotent Law: If a binary variable is ANDed with itself or ORed with itself, the binary
value of the output will be that of the input variable.
AA = A
A + A = A
(5) The Distributive Law
:
A(B + C) = AB + AC
A + BC = (A + B)(A + C)
(6) De Morgan’s Law
: Inversion or negation of a Boolean expression may be accomplished by
negating each variable/constant and by changing each AND to OR and OR to AND.
_ _ _ _
A • B = A + B
_ _ _ _
A + B = A • B
(7) The Law of Absorption
:
A + AB = A
A(A + B) = A
(8) The Law of Expansion
:
_
AB + AB = A
_ _
A(B + B) = (B + B = 1)
A(l) = A
_
(A + B)(A + B) = A
Q-6. Number Systems.
a. Introduction
. The number of different symbols of digits used in a number system is called the
base (or radix) of the system. A number system is possible with any base larger than one, but only a few
number systems have any practical applications.
(1) Commonly used systems are the binary (base 2), the octal (base 8), the decimal (base 10), and
the hexadecimal (base 16). The subscript of a number indicates the base. Some examples are 23
8
, 14
10
,
and 1001
2
.
(2) Theoretically, digital computers can be designed to work with any number system, but the
binary number system is most commonly used since it is easily adaptable to simple circuits. The use of