Wiki
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.
Within Information Technology (IT) there are many fields and subjects that compose the digital landscape, many iterations progressed to the current systems we have today. The focus of this site will be much more narrow only including areas in which I (Syl) become fixated on or otherwise have learned about. The primary areas will be focused on query languages and Boolean logic as it’s used in my daily life.
Boolean Algebra is a branch of algebra that handles mathematical expressions for true and false values, usually labeled 1 and 0 respectively. It is used to simplify and analyze logical expressions, particularly in digital circuits and computer science. Using algebraic laws can help us simplify logical expressions to make more efficient and useful logic whether it’s in circuit form or expressed via natural language.
Logic in this context would refer to a system of rules which allows us to manipulate those values to produce a desired outcome. In languages, logic is commonly used as ways to help communicate reasoning, such as “If this were to happen then this happens”, “I could eat this sandwich or this yogurt”, “You can have a salad and dessert.”
Properties & Laws
Temp
- BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
- In Boolean Algebra, Order of Operations applies to bracketed clauses first and then the query can be read left to right how we’d want it to.
Temp
Temp
AND - * “And” ”&” “A and B” OR - + “Or” ”|” “A or B” NOT “not” ”!” “A != B” “Not A and B” NOR - Not Or - Or Gate followed by a Not Gate - Output is 1 only when both inputs are 0 Complement of A or B and NOT(A or B) NAND - Not And - Not gate followed by an And gate. Output is 0 when non of inputs are 0. Complement of A and B and NOT (A and B) XOR - Exclusive-OR - accepts more than 2 inputs but only outputs 1 value. A bar and B or A and B bar - (A barB) + (A * B bar) and (((NOT A) and B) or (A and(NOT B))) XNOR - Exclusive-NOR - accepts more than 2 inputs but only outputs 1 value. A and B or A bar and B bar - (AB) + (A bar*b Bar) and (NOT (A and B) or (A and B))