What is the NOT logical operator like?
It has one input and one output, the output is opposite the input
What is the AND logical operator like?
Two inputs, one output. If both inputs are on then output is on otherwise no
What is the OR logical operator like?
It has two inputs and one output. Output is 1 if either A or B is 1
What is the XOR logical operator like?
It has two inputs and one output. The output is 1 if A or B are on but not both or none
What are truth tables?
Tables that lost all possible outcomes of logical expressions
What is boolean algebra?
a system of mathematics based on logic that has its own set of rules or
laws that can be used to simplify Boolean expressions
How are NOT, AND, OR, XOR gates represented in boolean algebra?
NOT: Ā(NOT A is Ā)
AND: . (A AND B A.B)
OR: + (A OR B A + B)
XOR: ⊕ (A XOR B A⊕B)
What does annulment law state?
A.0 = 0 A variable AND 0 is always equal to 0
A + 1 = 1 A variable OR 1 is always equal to 1
What does identity law state?
A + 0 = A A variable OR 0 is always equal to the variable
A.1 = A A variable AND 1 is always equal to the variable
What does Idempotent law state?
A + A = A A variable OR itself is always equal to the variable
A.A = A A variable AND itself is always equal to the variable
What does complement law state?
A.Ā = 0 A variable AND its complement is always equal to 0
A + Ā = 1 A variable OR its complement is always equal to 1
What does commutative law state?
A.B = B.A The order of two variables with AND makes no difference
A + B = B + A The order of two variables with OR makes no difference
What does double complement law state?
Double Complement Law
NOT NOT A = A A double complement of a variable is always equal to the variable
What does distributive law state?
A(B + C) = A.B + A.C (OR Distributive law)
A + (B.C) = (A + B).(A + C) (AND Distributive law)
What does absorptive law state?
A + (A.B) = A (OR Absorption law)
A(A + B) = A (AND Absorption law)
What does associative law state?
A + (B + C) = (A + B) + C = A + B + C (OR Associative law)
A(B.C) = (A.B)C = A.B.C (AND Associative law)