Truth tables, Logic evaluation rules, Boolean logic rules – Rockwell Automation T6200 Compressor Anti-Surge and Capacity Controller User Manual
Page 189
Data Structures and Expressions
A-11
Truth Tables
Logic Evaluation Rules
Commutative Property:
A & B = = B & A
A | B = = B | A
Associative Property:
A & (B & C) = = (A & B) & C
A | (B | C) = = (A | B) | C
Distributive Property:
A & (B | C) = = (A & B) | (A & C)
A | (B & C) = = (A | B) & (A | C)
Absorptive Property:
A & (A | B) = = A
A | (A & B) = = A
DeMorgan's Theorem:
-(A & B & C) = = -A | -B | -C
-(A | B | C) = = -A & -B & -C
XOR Identity:
A ^ B = = (-A & B) | (A & -B)
-(A^B)= =A^B= =-A^B
= = (-A & B) | (A & B)
Theorems:
A & 0 = = 0 A & 1 = = A
A | 0 = = A A | 1 = = 1
A & A = = A A & -A = = 0
A | A = = A A | -A = = 1
Boolean Logic Rules
Expression
Result
-0
-1
A&0
A&1
A&A
A&-a
A|0
A|1
A|A
A|-A
A&A (A|B)
A|A (A&B)
= =1
= =0
= =0
= =A
= =A
= =0
= =A
= =1
= =A
= =1
= =A
= =A
NOT
A
-A
0
1
1
0
OR
A
B
A|B
0
0
1
1
0
1
0
1
0
1
1
1
AND
A
B
A&B
0
0
1
1
0
1
0
1
0
0
0
1
XOR
A
B
A^B
0
0
1
1
0
1
0
1
0
1
1
0