This key facts covers Common Boolean Identities (Simplification Rules) within Boolean Expressions for GCSE Computer Science. Revise Boolean Expressions in 3.4 Computer Systems for GCSE Computer Science with 17 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 10 of 12 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Common Boolean Identities (Simplification Rules)
Some Boolean expressions can be simplified using mathematical identities:
| Identity Name | Expression | Simplifies To | Explanation |
|---|---|---|---|
| Identity Law | A AND 1 | A | ANDing with 1 doesn't change A |
| Identity Law | A OR 0 | A | ORing with 0 doesn't change A |
| Null Law | A AND 0 | 0 | ANDing with 0 always gives 0 |
| Null Law | A OR 1 | 1 | ORing with 1 always gives 1 |
| Complement Law | A AND NOT(A) | 0 | Contradiction - can't be both true and false |
| Complement Law | A OR NOT(A) | 1 | Tautology - always true (A is either 1 or 0) |
| Double Negation | NOT(NOT(A)) | A | Two NOTs cancel out |
| Absorption | (A AND B) OR A | A | If A is true, whole expression is true |
Practice questions for Boolean Expressions
Which Boolean operator produces an output of 1 only when BOTH inputs are 1?
State De Morgan's first law and give an example to illustrate it.