Logic expressions and circuits
Logic expressions and circuits
- Gates are combined into logic circuits to carry out a task.
- The same logic can be a problem statement, an expression, a circuit, or a truth table.
- You must move between all four.
Logic expressions
- 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.
Practice
The expression (A AND B) OR (NOT C) means:
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.
Practice
For X = (A AND B) OR C with A=1, B=0, C=1, what is X?
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.
Practice
"An alarm X sounds when the door is open (A) AND the system is on (B)." The expression is:
The word "AND" with two conditions gives a single AND gate: X = A AND B.
Practice
How many rows does a truth table have for a circuit with 3 inputs?
Each input doubles the combinations: 2^3 = 8 rows (000 to 111).
Practice
When drawing a circuit from a problem statement, you should:
At IGCSE you draw the circuit as described — simplification is not required.
You've got it
Key idea
- 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