Appendix A - Logic Operations; I - And (Logical Conjunction) - Makel MSA-CM Series User Manual

APPENDIX A -
Each of the Lighting Channels can have one logic input (see 4.2.1), that can be used to control the output
status of the channel. In here, useful theoretical information about the four logic operations will be
presented.
These functions belongs to the algebra's subarea Boolean algebra, in which the values of the variables are
the truth values TRUE and FALSE, that commonly are denoted by '1' and '0', respectively.

I - AND (Logical Conjunction)

This operator can be represented by the symbol " ".
its operands are TRUE, otherwise the value is FALSE.
Main properties:
• Commutativity:
A∧( B∧C)⇔( A∧B)∧C
• Associativity:
A∧(B∨C)⇔( A∧B)∨(A∧C )
• Distributivity:
Input Output
A B
0
0
1
1
User's Manual
LOGIC OPERATIONS
A∧ B⇔ B∧ A
;
Table 10: Truth tables for Conjunction Operation
A∧B A B C A∧B C
0 0 0 0 0
1 0 0 0 1
0 0 0 1 0
1 1 0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
∧ A n-place logical operator AND results TRUE if n of
;
;
Output Input
A B C D A∧B C D
∧
0 0 0 0 0
0 0 0 0 1
0 0 0 1 0
0 0 0 1 1
0 0 1 0 0
0 0 1 0 1
0 0 1 1 0
1 0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Appendixes
Output
∧ ∧
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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