Logic expressions and circuits
Introduced| English | Meaning |
|---|---|
| logic circuit/ˈlɒdʒɪk ˈsɜːkɪt/ | A combination of logic gates connected to implement a Boolean function. |
| problem statement/ˈprɒbləm ˈsteɪtmənt/ | A clear description of the problem to be solved and the required outcome. |
| truth table/truːθ ˈteɪbl/ | A table listing the output of a logical expression or circuit for every combination of inputs. |
| logic expression/ˈlɒdʒɪk ekˈspreʃn/ | An expression combining Boolean values or conditions to produce a true or false result. |
From statement to circuit
- Gates are combined into logic circuits 逻辑电路 to carry out a task.
- The same logic can be a problem statement 问题陈述, an expression, a circuit, or a truth table 真值表.
- You must move between all four.
Logic expressions 逻辑表达式
- A logic expression writes a circuit using letters and gate words.
- e.g.
(A AND B) OR (NOT C)means: doA AND B, doNOT C, then OR the two results.
Logic gates are built from electronic circuits like this one.
OR outputs 1 when either input is 1
Logic expressions & circuits
gates combine into circuits
Each gate has a rule; combine them to build a circuit — explore one gate at a time.
The expression (A AND B) OR (NOT C) means:
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Work out each part — (A AND B) and (NOT C) — then OR them together.
Logic circuits
- A logic circuit joins gates: the output of one gate becomes the input of another.
- At IGCSE a circuit has up to three inputs and one output.
For X = (A AND B) OR C with A=1, B=0, C=1, what is X?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
A AND B = 0; 0 OR C(=1) = 1, so X = 1.
From statement to truth table
- Problem → circuit: pick out the conditions and the logic words. "An alarm (X) sounds when the door is open (A) AND the system is on (B)" →
X = A AND B. - Completing a truth table: write all input combinations (3 inputs → 8 rows), work out each gate's output column in order, and the last column is the final output.
- Draw the circuit exactly as stated — don't simplify it.
The circuit for X = (A AND B) OR C: the AND gate's output becomes one input of the OR gate.
Match each English phrase to its logic expression.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Turn the words into gates: "and" → AND, "or" → OR, "not" → NOT, "exactly one" → XOR.
How many rows does a truth table have for a circuit with 3 inputs?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Each input doubles the combinations: 2^3 = 8 rows (000 to 111).
When drawing a circuit from a problem statement, you should:
Difficulty 1/5 · 100 coins + a small bonus on first completion today
At IGCSE you draw the circuit as described — simplification is not required.
You've got it
- a logic expression uses letters + AND/OR/NOT; a circuit chains gates (≤3 inputs, 1 output)
- turn a problem statement into an expression by spotting the logic words
- a truth table has $2^n$ rows ($n$ inputs); add a working column per gate
- draw the circuit exactly as stated, without simplifying