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Propositional Logic and Hardware Implementation — Class 11 ISC Computer Science revision notes

A 4-page visual revision sheet for Propositional Logic and Hardware Implementation, written for Class 11 ISC Computer Science. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

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Propositional Logic and Hardware Implementation in one look

from a sentence that is true or false, to the gates that add two numbers

A proposition is a sentence with a truth value

  • a propositional variable stands for a statement that is either true or false, never both and never neither
  • connectives build bigger statements: NOT for negation, AND for conjunction, OR for disjunction, then implication and equivalence
  • a well formed formula is one built by the rules: variables are wff, and if p and q are wff then so are NOT p, p AND q, p OR q and the rest, with brackets making the grouping explicit
  • an interpretation assigns true or false to every variable, and the formula then has one truth value under it

The five connectives

  • NOT p: negation, true exactly when p is false
  • p AND q: conjunction, true only when both are true
  • p OR q: disjunction, true when at least one is true, so it is the inclusive or
  • p implies q: false only when p is true and q is false, true in every other case including when p is false
  • p equivalent q: true when both sides carry the same truth value

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