Logical Operations Flashcards
NOT logical operator.
0 = 1 1 = 0
AND logical operator.
0 + 0 = 0
0 + 1 = 0
1 + 0 = 0
1 + 1 = 1
OR logical operator.
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
XOR logical operator.
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0
What are the laws of Boolean algebra?
- System of mathematics based on logic that has its own set of rules or laws that can be used to simplify Boolean expressions.
- on top of a letter in Boolean algebra.
- A bar on top of an input variable represents the NOT operator. = NOT A
. in Boolean algebra.
- Represents the AND operator. A and B = A.B
+ in Boolean algebra.
Represents the OR operator. A or B = A + B
+ sign with a circle in Boolean algebra.
Represents the XOR operator. A exclusive or B = A + () B.
Annulment law in Boolean algebra.
A.0 = 0 (A variable AND 0 = 0)
A + 1 = 1 (A variable OR 1 = 1)
Identity law in Boolean algebra.
A + 0 = A (A variable OR 0 = A variable)
A.1 = A (A variable AND 1 = A variable)
Idempotent law in Boolean algebra.
A + A = A (A variable OR A variable = A variable)
A.A = A ( A variable AND A variable = A variable)
Complement law in in Boolean algebra.
A.(-on top)A = 0 (A variable AND NOT A variable = 0
A +(-on top)A = 1 (A variable OR NOT A = 1)
Commutative law in Boolean algebra.
A.B = B.A (A AND B = B AND A)
A + B = B + A (A OR B = B OR A)
Double complement law in Boolean algebra.
2NOT A = A (Double complement of a variable is always equal to the variable).
