Three tasks: circuit, table, expression
Section 10 converts between four forms: a problem statement, a logic expression, a logic circuit and a truth table. The three tasks: (a) draw a circuit, (b) complete a truth table, (c) write an expression — each from any of the others. Circuits use max 3 gates and 3 inputs. A truth table with inputs has rows: 2 inputs -> 4, 3 inputs -> 8 (no header). Write rows in binary order ().
The six logic gates
A logic gate takes binary inputs (0/1) and gives one output. 0478 uses six: NOT outputs the opposite of its input; AND = 1 only when both inputs are 1; OR = 1 when at least one is 1; NAND is NOT-AND (0 only when both are 1); NOR is NOT-OR (1 only when both are 0); XOR (EOR) = 1 when the inputs are different. Get NAND/NOR by flipping AND/OR's output bits. Each gate has a standard symbol (section 4) to draw exactly.
Complete a truth table column by column
To complete a truth table, add one working column per gate, then combine for the output — never evaluate the whole thing in one step. For build columns , then , then , then , working first gates / innermost brackets first. Intermediate columns earn method marks even if the final column slips. Check all rows are in binary order.
Drawn from real examiner reports.
Wrong gate symbol / missing bubble
When drawing gates or matching symbols, symbol errors recur. The XOR symbol is the OR shape with an extra curved line across the inputs — candidates invent variations or draw a plain OR. NAND/NOR are the AND/OR shapes with a small bubble on the output to show inversion; forgetting the bubble turns NAND into AND. Use the standard section-4 symbols only.
June 2023 Paper 2 Q9(a): identifying gate symbols was mostly well done, but "a few incorrectly identified the XOR gate with many different variations of this."
NOT-gate in the wrong place
A common circuit error is placing the NOT gate on the wrong line or in the wrong order — e.g. inverting the combined output instead of inverting a single input first. Wire the gates strictly in the order the expression's brackets dictate: gates on the raw inputs first, then the gates that combine their results.
June 2022 Paper 2: a circuit error was "the incorrect placement of the NOT gate before the XOR gate."
AND vs OR: all vs any
Candidates often name a gate correctly but write the wrong truth table. AND vs OR: AND outputs 1 only when BOTH inputs are 1; OR outputs 1 when AT LEAST ONE is 1 — "AND = all, OR = any." Writing OR's table for an AND gate (or the reverse) scores zero. They agree only on (both 0) and (both 1).
June 2022 Paper 2: candidates "named correct logic gates but confused the logic tables for the gates." November 2022 Paper 2 Q7(a): identifying the statement for each gate — "the most common incorrect response was for the second statement."
NAND vs NOR: flip AND vs flip OR
NAND vs NOR are easy to swap. NAND is NOT-AND (0 only when both inputs are 1, otherwise 1); NOR is NOT-OR (1 only when both inputs are 0, otherwise 0). Quick check: take AND's output column and flip every bit for NAND; take OR's column and flip every bit for NOR. Both symbols carry an output bubble, but they are different gates.
XOR is not OR
XOR (EOR) is not OR. XOR outputs 1 when the inputs are different and 0 when they are the same. It matches OR on three rows but differs on : OR gives 1, XOR gives 0. Treating XOR like OR (outputting 1 for two 1s) is the classic XOR error.
Wrong number of truth-table rows
A truth table with inputs must list all input combinations in binary order. Errors: a 3-input table needs 8 rows (not 9 — do not count the header row); rows written out of order, so a combination is repeated or missed. When asked how many rows, give — for 3 inputs, 8. Count up in binary ().
Truth table: work column by column
Completing a truth table: write the inputs first in binary order ( rows), then one working column per gate in evaluation order (first gates / innermost brackets first), then the output. Fill a whole column at a time, not a row — faster and less error-prone.
Draw a circuit in bracket order
Drawing a circuit: the brackets give the order — draw the gates on the raw inputs first, then feed their outputs into the next gate. Use the exact section-4 symbols: a bubble on NAND/NOR outputs, the extra line for XOR. Label every input () and the output.
Write an expression by tracing paths
Writing an expression: follow each path through the circuit from inputs to output, writing AND/OR/NOT/NAND/NOR/XOR for each gate and bracketing each sub-result, until you reach the final output. Brackets show which gate acts first.
Fast gate checks
Fast gate checks: AND = "all 1s"; OR = "any 1"; XOR = "inputs different -> 1"; NAND = "flip AND"; NOR = "flip OR". Use these to fill or verify a column quickly and to spot a gate whose truth table you have mixed up.
A logic gate takes one or more binary inputs (each 0 or 1) and produces a single binary output following a fixed rule. Real processors are built from millions of these gates. The 0478 syllabus uses six gates: NOT, AND, OR, NAND, NOR, XOR (also written EOR). You must know each gate's function, its standard symbol (defined in section 4 of the syllabus — used when drawing circuits) and its truth table.
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