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Knowledge/A Level/H446/01 Computer systems/Boolean Algebra/Define problems using Boolean logic

Define problems using Boolean logic

Define problems using Boolean logic. See appendix 5d

1.4.3 Boolean Algebra

Boolean Algebra — Note 1 of 5

Candidates should be familiar with AND, OR, NOT and XOR. Candidates should be familiar with the logic of each Boolean operator, and the truth tables. Candidates should be able to define problems using Boolean logic, using the notation in appendix 5d.

What you need to know

Boolean logic expresses conditions that are either true or false, combined using operators such as AND, OR, NOT and XOR. You need to be able to turn a written problem into a Boolean expression using OCR's notation.

What to know

  • Conjunction (AND): A ∧ B is true only when both A and B are true. Alternatives accepted: A AND B, A.B.
  • Disjunction (OR): A ∨ B is true when at least one of A or B is true. Alternatives: A OR B, A + B.
  • Negation (NOT): ¬A is true when A is false. Alternatives: NOT A, ~A, A with a bar over it.
  • Exclusive disjunction (XOR): A ⊻ B is true when exactly one of A or B is true. Alternatives: A XOR B, A ⊕ B.
  • Equivalence: ≡ (or ↔) shows that two expressions always give the same result.
  • Order of precedence: brackets, then NOT, then AND, then OR.

Exam technique

  • Tip:Use brackets to make the intended order clear, especially when AND and OR appear together.
  • Example:'The alarm (Q) sounds if the system is armed (A) and either the door (B) or the window (C) is opened': Q = A ∧ (B ∨ C).
← Previous topicHow to create, traverse, add data to and remove data from these data structures1.4.2 Data StructuresNext note →Manipulate Boolean expressions, including the use of Karnaugh maps1.4.3 Boolean Algebra

Back to Boolean Algebra

Boolean Algebra

Note 1 of 5

  1. 1Define problems using Boolean logic
  2. 2Manipulate Boolean expressions, including the use of Karnaugh maps
  3. 3De Morgan's Laws, distribution, association, commutation and double negation
  4. 4Using logic gate diagrams and truth tables
  5. 5The logic associated with D type flip flops, half and full adders
Topic overview