Computing - Boolean Algebra
Boolean Algebra
Boolean algebra is like writing algebraic expressions acting on variables. Boolean notation is the set of symbols that define logical operators on variables.
\[P = \text{NOT} (A \text{AND} B) P = \overline{A \cdot B}\] \[P = (A \text{AND} B) \text{OR} C P = (A \cdot B) + C\]NOT
\[P = \text{NOT} A P = \overline{A}\]AND
\[P = A \text{AND} B P = A \cdot B\]OR
\[P = A \text{OR} B P = A + B\]XOR
\[P = A \text{XOR} B P = A \oplus B\]NOR and NAND
Instead of having a special notation, you write these as boolean expressions themselves.
\[P = \text{NOT} (A \text{OR} B) P = \overline{(A + B)}\]What is the order of operations for boolean algebra?
- Highest: NOT
- Middle: AND
- Lowest: OR
De Morgan’s Laws
Who was Augustus De Morgan?
August De Morgan was a mathematician who invented laws to simplify boolean expressions.
What is De Morgan’s first law?
What is $\overline{A} \cdot \overline{B}$ equivalent to?
What is De Morgan’s second law??
\[\overline{A \cdot B} = \overline{A} + \overline{B}\]What is $\overline{A \cdot B}$ equivalent to?
In boolean algebra, simplify $X \cdot 0
$$?? $0$
What is the commutative rule?
The order of operations does not matter.
Because of the commutative rule, what is $X \cdot Y$ equivalent to?
What is the associative rule?
Doing _ _ A _ _ then _ _ B _ _ is the same as doing _ _ B _ _ then _ _ A _ _ .
Because of the associative rule, what is $X \cdot (Y \cdot Z)$ equivalent to?
What is the distributive rule?
Applying an operand to a bracket is the same as applying the operand to each term of the bracket.