Boolean Algebra — Class 12 ISC Computer Science revision notes
A 4-page visual revision sheet for Boolean Algebra, written for Class 12 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.
Page 1 as PDF
Boolean Algebra in one look
the laws that shrink an expression, and the map that does it without algebra
Two values, three operations, one algebra
- a Boolean variable takes exactly two values, written 0 and 1 or false and true, and there is nothing in between
- the three operations are AND written as a product, OR written as a sum, and NOT written as a bar over the term
- every law below can be proved by truth table, which is the method the paper accepts when it says verify
- the algebra is not ordinary arithmetic: 1 + 1 is 1 here, because + means OR
The postulates and the basic theorems
- operations with 0 and 1
A + 0 = A, A + 1 = 1, A . 0 = 0, A . 1 = A - complements
A + A' = 1, A . A' = 0 - idempotence
A + A = A, A . A = A - involution
(A')' = A - commutativity
A + B = B + A, A . B = B . A - associativity
A + (B + C) = (A + B) + C - distributivity
A . (B + C) = A.B + A.C, A + B.C = (A + B).(A + C) - absorption
A + A.B = A, A . (A + B) = A - De Morgan
(A.B)' = A' + B', (A + B)' = A' . B'
Duality, which halves what has to be learnt
- swap every AND with OR and every 0 with 1, leave the variables alone, and a true statement stays true
- so A + 0 = A has the dual A . 1 = A, and the two absorption laws are duals of each other
- the complement of an expression is not its dual: complementing also bars every variable, which is De Morgan
- in the exam, proving one of a dual pair is normally enough to claim the other, but say so explicitly
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Boolean Algebra sheet covers
- Two values, three operations, one algebra
- The postulates and the basic theorems
- operations with 0 and 1
- complements
- idempotence
- involution
- commutativity
- associativity
- distributivity
- absorption
- De Morgan
- Duality, which halves what has to be learnt
- sum of products
- product of sums
- Minterms, maxterms, and the two canonical forms
- Canonical against cardinal notation
- Canonical
- Cardinal
- The Karnaugh map, and why the headers are not in counting order
- Reducing with a map, in order
- Fill
- Group
- Read
- Sum
- well formed formula
- propositional logic
- Implication, and the three sentences that are not it
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Computer Science chapter by chapter against your real exam dates and free hours, and when the plan reaches Boolean Algebra the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.