The big idea: A logic diagram shows the gates and the wires between them — what feeds what.
Signals travel left to right: inputs on the left, gates in the middle, the output on the right.
The same thing, drawn: A worded rule, a Boolean expression, a truth table and a logic diagram all carry identical information.
The exam moves you between them, so being fluent in all four is the skill.
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X = (A AND B) OR NOT C, drawn and then read. Notice how the two middle signals meet at the OR gate.
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1 — Write the expression first
Turn the rule into Boolean form before drawing anything.
"The motor runs if the guard is closed and the switch is on, unless the override is active" becomes M = G·S·(NOT O).
2 — Draw the inputs down the left
One labelled line per input, stacked vertically, with room between them.
Draw them all before any gate — it stops wires crossing later.
3 — Work outwards from the brackets
Whatever is inside brackets happens first, so draw those gates first.
Here the NOT gate on O comes first, because its result is needed before the final AND.
4 — Join the results into the final gate
Feed each gate's output into the next gate's input, and label the output line.
Then read your own diagram back left to right and check it says what the rule said.
Use the standard symbols: A flat-backed D shape is AND. A curved back with a pointed front is OR. A triangle with a circle is NOT.
A circle on the output turns any gate into its inverted version, and an extra curve at the back makes it exclusive.
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Simplify before you draw: A shorter Boolean expression is a smaller diagram: fewer gates, less hardware, less power.
Simplifying first also means fewer wires to draw and fewer chances to slip.
Rules worth knowing
- A·A = A and A + A = A
- A·1 = A and A + 0 = A
- A·0 = 0 and A + 1 = 1
- A + (NOT A) = 1 and A·(NOT A) = 0
The two that save most
- A + A·B = A — if A alone is enough, drop the rest
- A·(B + C) = A·B + A·C — factor out what is common
- Both remove whole gates from the drawing
- Look for a repeated letter; that is the clue
Always check
- Build the truth table for the original
- Build it for your simplified version
- Every row must match, or the simplification is wrong
- This catches nearly every error
Simplified is not always simpler to build: Fewer terms usually means fewer gates, but not always fewer types of gate.
Real circuits are often rebuilt from NAND gates alone, because one repeated component is cheaper than several different ones.
How this is tested — you must draw correct standard symbols and wire them in the right order. It comes up two ways:
Paper 1 Section A
- Construct a logic diagram from a rule or an expression, 3-5 marks
- Write the expression for a given diagram
- Simplify, then draw the smaller circuit
Paper 1 Section B — case study
- Draw the control logic for a case study system
- Explain what each gate contributes to the rule
The classic trap: Drawing the gates in the wrong order. Brackets happen first, so a gate inside brackets must feed the gate outside them — not the other way round. Read your own diagram back before moving on.
A greenhouse vent opens when the temperature is high and the wind sensor is not triggered, or when the manual override is on. Construct a logic diagram using H, W and M.
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