Computing - Boolean Algebra
AQA Computer Science 2022
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?
Simplification identities
The commutative, associative and distributive rules
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.