Worksheets › Class 11 › Boolean Logic › Cheat sheet
Class 11 Boolean Logic: cheat sheet
CBSE Computer Science. The gates NOT, AND, OR, NAND, NOR and XOR, truth tables, De Morgan’s laws and two-gate circuits, every output worked out row by row.
Key ideas
- A truth table lists every combination of inputs: n inputs give 2ⁿ rows, written in order from 00…0 to 11…1.
- AND gives 1 only when every input is 1; OR gives 0 only when every input is 0; NOT turns its one input round.
- NAND is AND followed by NOT and NOR is OR followed by NOT; each is a universal gate, able to build every other gate.
- XOR gives 1 when its two inputs are different (with more inputs, when an odd number of them are 1).
- Work out an expression in the order: brackets, then NOT, then AND, then OR.
- Two expressions are equal only if their output columns agree in every row of the truth table.
- In a circuit, find the first gate’s output for each row, then use it as an input of the next gate.
Remember
| Outputs for 00, 01, 10, 11 | AND 0, 0, 0, 1; OR 0, 1, 1, 1; XOR 0, 1, 1, 0 |
| The inverted gates | NAND 1, 1, 1, 0; NOR 1, 0, 0, 0 |
| De Morgan’s laws | NOT (A AND B) = NOT A OR NOT B; NOT (A OR B) = NOT A AND NOT B |
| Always the same | A OR NOT A = 1; A AND NOT A = 0; NOT (NOT A) = A; A OR (A AND B) = A |
| Written as symbols | A + B is A OR B; A · B is A AND B |
| Rows giving 1, gate of n inputs | AND, NOR: just one; OR, NAND: all but one; XOR: half of them |
Watch out
- Putting NOT on each part without changing AND to OR (or OR to AND).
- Mixing up NOR (1 only when every input is 0) with XOR (1 when the inputs differ).
- Writing 6 rows for three inputs: there are 2 × 2 × 2 = 8.
- Doing OR before AND: A OR B AND C means A OR (B AND C).
Worked example
For A = 0 and B = 1, find (a) NOT (A AND B) (b) NOT A OR NOT B (c) NOT (A OR B) (d) NOT A AND NOT B.
Working: (a) and (b) are always equal, and so are (c) and (d): De Morgan’s laws
Answer: (a) 1; (b) 1; (c) 0; (d) 0
Practise Boolean Logic
Revise with this page, then practise: every Boolean Logic sheet in the app is new, with an answer key and working.
Coming soon for Android and iPhone.