Appendixes
II - OR (Logical Disjunction)
This operator can be represented by the symbol “ ”. A
∨
n
-place logical operator AND results
TRUE
if at
least 1 of
n
operands is
TRUE
, if
n
operands are
FALSE,
then the result is
FALSE.
Main properties:
•
Commutativity:
A
∨
B
⇔
B
∨
A
;
•
Associativity:
A
∨(
B
∨
C
)⇔(
A
∨
B
)∨
C
;
•
Distributivity:
A
∨(
B
∧
C
)⇔(
A
∨
B
)∧(
A
∨
C
)
;
Table 11: Truth tables for Disjunction Operation
Input Output
Output
Input
Output
A B
A
∨
B
A B C A
∨
B C
∨
A B C D A
∨
B C D
∨ ∨
0 0
0
0 0 0
0
0 0 0 0
0
0 1
1
0 0 1
1
0 0 0 1
1
1 0
1
0 1 0
1
0 0 1 0
1
1 1
1
0 1 1
1
0 0 1 1
1
1 0 0
1
0 1 0 0
1
1 0 1
1
0 1 0 1
1
1 1 0
1
0 1 1 0
1
1 1 1
1
0 1 1 1
1
1 0 0 0
1
1 0 0 1
1
1 0 1 0
1
1 0 1 1
1
1 1 0 0
1
1 1 0 1
1
1 1 1 0
1
1 1 1 1
1
III -
XOR (Exclusive disjunction)
This operator can be represented by the symbol “
⊕
”. A
n
-place logical operator XOR results
TRUE
if one
odd number of operands is
TRUE
, otherwise the result is
FALSE.
Main properties:
•
Commutativity:
A
⊕
B
⇔
B
⊕
A
;
•
Associativity:
A
⊕(
B
⊕
C
)⇔(
A
⊕
B
)⊕
C
;
User’s Manual
Page 41
