YOUR TOPIC 10 REVISION ROUTE
Start by recognising each gate and explaining its rule. Then follow those rules through connected gates. A circuit, an expression and a truth table are three ways to describe the same decision.
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01 | DEFINE THE SIGNAL BEFORE USING IT
Boolean values are TRUE and FALSE, represented here by 1 and 0. The meaning of 1 depends on the input definition: DoorOpen = 1 means open, whereas DoorClosed = 1 means closed.
A gate applies a fixed rule to its inputs. Letters name signals, rather than fixing their values. Read standard symbols with inputs on the left and output on the right. NOT takes one input; the other syllabus gates use two.
Logic is not ordinary arithmetic. OR with inputs 1 and 1 gives one Boolean result, 1, not the number 2. XOR with those same inputs gives 0 because it requires exactly one true input.
02 | RECOGNISE ALL SIX SYMBOLS
AND has a flat input side and rounded output. OR has a curved input side and pointed output. XOR adds a second curved line on the input side. NOT is a triangle with an output circle.
The small circle means inversion: reverse 0 and 1. NAND is an AND symbol with an output circle; NOR is OR with that circle.
03 | REMEMBER THE RULE, NOT ONLY THE NAME
| Gate | When output is 1 | Example |
|---|---|---|
| NOT | Its single input is 0 | NOT 0 = 1 |
| AND | Both inputs are 1 | 1 AND 0 = 0 |
| OR | At least one input is 1, including both | 1 OR 1 = 1 |
| XOR / EOR | Exactly one input is 1 | 1 XOR 1 = 0 |
| NAND | The inputs are not both 1 | NOT (1 AND 0) = 1 |
| NOR | Neither input is 1 | NOT (0 OR 0) = 1 |
OR and XOR agree on 00, 01 and 10; they differ on 11. “At least one” includes both, whereas “exactly one” excludes both. NAND and NOR reverse their whole AND or OR result, not just one input.
04 | COMPLETE EVERY INPUT COMBINATION
One input has two combinations, 0 and 1. Two inputs have four: 00, 01, 10 and 11. Each row is a separate possible situation, not an instruction sequence.
| A | NOT A |
|---|---|
| 0 | 1 |
| 1 | 0 |
| A | B | AND | OR | XOR | NAND | NOR |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 |
Use the paired columns as checks: AND and NAND must differ on every row, as must OR and NOR. XOR gives 1 for different input values and 0 for equal input values.
05 | CONNECT RULES TO THEIR INPUT DEFINITIONS
For A = MovementDetected and B = Dark, a light requiring both conditions uses A AND B. An alarm triggered by smoke or heat uses OR if either or both should trigger it.
“Neither active” uses NOR. “Exactly one selected” uses XOR. Inverting one proposition uses NOT. Define the true state of every signal before translating the wording.
If B = WindowOpen but the requirement needs a closed window, use NOT B. If B already means WindowClosed, use B directly. The wording of the input is part of the problem.
06 | CIRCUIT, EXPRESSION AND TRUTH TABLE
A circuit shows gate connections. An expression writes the Boolean rule. A truth table lists the output for all possible external input combinations. You should be able to construct or interpret each from the others.
The syllabus uses circuits with up to three external inputs and one final output. Every gate other than NOT still has two inputs: its inputs may be intermediate outputs from earlier gates.
Draw the circuit given by the statement or expression without simplification. An equivalent shorter circuit may not reproduce the requested structure.
07 | LABEL INTERMEDIATE SIGNALS
Here P = A AND B, Q = NOT C, and X = P OR Q. Substitute the first two expressions to get X = (A AND B) OR (NOT C).
P and Q are calculated values, not additional independent inputs. A wire carries its signal unchanged. A split supplies the same signal to multiple destinations; a junction dot marks an intentional connection where appropriate.
08 | FOLLOW ONE ROW BEFORE THE WHOLE TABLE
For 101, AND receives 1 and 0, giving P = 0. NOT receives C = 1, giving Q = 0. The final OR receives P = 0 and Q = 0, giving X = 0.
For 000, P is 0 but Q is 1, therefore X = 1. Do not feed C directly into the final OR when the circuit supplies NOT C.
| A | B | C | P = A AND B | Q = NOT C | X |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
Three binary inputs give eight combinations. In row order 000 through 111, A changes after four rows, B after two and C after each row. Start every row independently.
09 | GROUPING CAN CHANGE THE ANSWER
Compare X = (A AND B) OR (NOT C) with Y = A AND (B OR (NOT C)). X ends with OR; Y ends with AND and always requires A to be true.
| Inputs ABC | X | Y | Reason |
|---|---|---|---|
| 000 | 1 | 0 | NOT C enables X, but A blocks Y |
| 101 | 0 | 0 | Both final rules fail |
| 110 | 1 | 1 | Both routes meet their final conditions |
Read nested parentheses from the inner operations towards the final output. NOT (A AND B) reverses the completed AND result. (NOT A) AND B reverses only A before combining it with B.
10 | FROM A STATEMENT TO A CIRCUIT
A greenhouse fan runs when it is hot and the window is not open, or when manual override is selected. Let A = Hot, B = WindowOpen and C = ManualOverride.
First invert B. AND that result with A. Finally OR that result with C. The expression is X = (A AND (NOT B)) OR C.
| ABC | NOT B | A AND NOT B | X |
|---|---|---|---|
| 000 | 1 | 0 | 0 |
| 001 | 1 | 0 | 1 |
| 010 | 0 | 0 | 0 |
| 011 | 0 | 0 | 1 |
| 100 | 1 | 1 | 1 |
| 101 | 1 | 1 | 1 |
| 110 | 0 | 0 | 0 |
| 111 | 0 | 0 | 1 |
Check a case with override off to test the main route, and a case with override on to test the alternative route. Then check every combination.
11 | FROM A TRUTH TABLE TO AN EXPRESSION
Inspect the rows where output is 1. For outputs 0, 1, 1, 0 in two-input row order, exactly one input must be true, which identifies XOR.
To express the same rule using the true rows, 01 means (NOT A) AND B, and 10 means A AND (NOT B). OR these cases: X = ((NOT A) AND B) OR (A AND (NOT B)).
If asked to identify a single gate, XOR answers that table. If given the expanded expression and asked to draw it, retain the specified NOT, AND and OR structure.
For a three-input table with output 1 only on 110 and 111, A and B must both be true but C does not affect the result. The rule is A AND B. If only 110 is true, include NOT C as a further requirement using two-input gates.
COMMON MISTAKES | CHECK YOUR THINKING
- Treating 1 as always “safe” rather than using the defined meaning.
- Confusing inclusive OR with exactly-one XOR.
- Missing the inversion circle or the extra XOR input curve.
- Inverting one input when the whole combined result should be inverted.
- Feeding an external input into a later gate instead of its intermediate result.
- Choosing intermediate signals independently of their source inputs.
- Omitting combinations or carrying values between truth-table rows.
- Ignoring parentheses or changed input definitions.
- Drawing a three-input AND or OR where two-input gates are required.
- Simplifying the given circuit instead of drawing the requested structure.
- Checking only 111 instead of every combination.
CHECK YOUR UNDERSTANDING WITHOUT NOTES
Draw all six symbols. Explain why OR and XOR differ for 11. Rebuild the worked circuit and its truth table, then change the grouping to A AND (B OR (NOT C)) and compare its output for 000.
Explain by connecting values to a rule: “The AND receives 1 and 0, so its output is 0 because both inputs must be true.” Compare both functions on the same combinations. Demonstrate a complete labelled circuit or a gate-by-gate calculation.
Mark uncertain cards, revisit their lesson links and then try a new set of input values.
End of topic review