← IGCSE Computer Science Paper 2

Drawing circuits without simplification

Draw every gate in the given expression, one for each operator, even if a shorter circuit has the same truth table. Never combine or remove gates.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 30

Understanding Drawing circuits without simplification in IGCSE Computer Science Paper 2

What it does: The expression has three operators (NOT, AND, OR), so the circuit has three gates, one for each operator. This expression needs two OR gates and one AND gate. Replacing it with A OR (B AND C) gives the same truth table but uses different gates, so it would lose marks. Every operator needs its own gate. Leaving out NOT C changes the circuit, so it must be drawn. There are two NOT operators, so two NOT gates must be drawn. Cancelling them out is simplifying, which the question does not allow.

Common mistakes: The expression has two operators, AND and OR, so the circuit needs two gates. It must not be squashed into one gate. It should say: Gates needed: 2. The circuit must be drawn exactly as the expression is given, with one gate for each operator. It must not be cut down to the fewest gates. It should say: Rule: one gate per operator.

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This module's key terms are also in a printable crossword (Modules 562–580) and word search (Modules 539–580).

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Learning
Duo
You are asked to draw a circuit for X = (A AND B) OR (A AND C). How many gates should your circuit contain?
Three: two AND gates and one OR gateTwo: A AND (B OR C) is shorter
Matches
Expression: X = (A AND B) OR (A AND B). Circuit drawn: one AND gate only, with output X
↓
The student removed the OR gate and one AND gate because both brackets are the same. The expression has three operators, so the circuit needs three gates.
Applying
Meanings
Term
one gate per operator
Meaning
Draw every gate in the given expression, one for each operator, even if a shorter circuit has the same truth table. Never combine or remove gates.
Practice
X = (A AND B) OR (NOT A AND B)
Testing
Gaps
Gates to draw: (two AND, one OR)
Check Answer
Spots
3Gate 2: OR takes Gate 1 and C
4Gates needed: 1

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Quick Questions

1. You are asked to draw a circuit for X = (A AND B) OR (A AND C). How many gates should your circuit contain?
A. Three: two AND gates and one OR gate ✓
B. Two: A AND (B OR C) is shorter
Draw one gate for each operator in the expression given. Here there are two ANDs and one OR, so three gates. Do not rewrite it as a shorter form.
2. A student draws a circuit with fewer gates than the expression has operators. The truth table is still identical. What mark outcome is likely?
A. Marks lost: the circuit does not match the expression ✓
B. Full marks: the truth table is the same
A circuit with the same truth table is not enough. The circuit must be drawn exactly for the expression given, using every gate.
3. The expression is X = NOT (A OR B). Which circuit is correct?
A. An OR gate with its output going into a NOT gate ✓
B. A single NOR gate
The expression has two operators, NOT and OR, so you draw two gates. A NOR gate combines them, which is not allowed when drawing the circuit as given.
4. The expression is X = (A AND B) OR NOT C. How many gates are needed?
A. Two: AND and OR, because NOT C can be left out
B. Three: AND, NOT and OR ✓
Every operator needs its own gate. Leaving out NOT C changes the circuit, so it must be drawn.
5. True or false: you should simplify an expression before drawing its circuit, to save gates.
A. True: shorter circuits are always preferred
B. False: draw the circuit exactly as the expression is written ✓
The question asks for a circuit for the given expression. Simplifying changes the gates used and is not what is asked.

Match the Pairs

X = (A AND B) OR (A AND C) → Draw two AND gates and one OR gate, three gates in total. Do not factor it into A AND (B OR C).
X = NOT (NOT A) → Draw two NOT gates in a row. Do not remove them, even though the output is the same as A.
Every operator in the expression needs its own gate, so this expression needs one NOT, one AND and one OR gate → X = (NOT A AND B) OR C
A circuit with the same truth table is not enough, because the circuit must use the gates of the given expression, such as an AND gate and an OR gate in this one → X = (A OR B) AND (A OR C)
Expression: X = (A AND B) OR (A AND B). Circuit drawn: one AND gate only, with output X → The student removed the OR gate and one AND gate because both brackets are the same. The expression has three operators, so the circuit needs three gates.
Expression: X = NOT (A AND B). Circuit drawn: one NAND gate with output X → The student combined the NOT and AND operators into one NAND gate. The expression has two operators, so it needs two gates: an AND gate followed by a NOT gate.

Key Term

one gate per operator
Draw every gate in the given expression, one for each operator, even if a shorter circuit has the same truth table. Never combine or remove gates.

Fill in the Blanks

1. X = (A AND B) OR (A AND C) Gates to draw: 3 (two AND, one OR)
Hint: Type the total number of gates, one for each operator in the expression.
2. X = NOT (A AND B) Draw AND then NOT, not one NAND gate
Hint: Type the name of the single combined gate that must not replace the two separate gates.
3. X = (A OR B) AND (A OR B) Gates: OR, OR and AND
Hint: Type the gate that joins the two bracketed parts. Do not reduce the expression to A OR B.
4. X = A AND (B OR C) Rule: one gate for each operator
Hint: Type the word for symbols such as AND, OR and NOT in an expression, each of which needs its own gate.
5. X = NOT (NOT A) Draw two NOT gates in series
Hint: Type, as a word, how many NOT gates must be drawn. Do not remove them to leave just A.

Spot the Error

Question 1
A Draw: X = (A AND B) OR C
B Gate 1: AND takes A and B
C Gate 2: OR takes Gate 1 and C
D Gates needed: 1
Line D — The expression has two operators, AND and OR, so the circuit needs two gates. It must not be squashed into one gate. It should say: Gates needed: 2.
Question 2
A Rule: use the fewest gates
B X = (A AND B) OR (A AND C)
C Gates: AND, AND, OR
D Draw all 3 gates
Line A — The circuit must be drawn exactly as the expression is given, with one gate for each operator. It must not be cut down to the fewest gates. It should say: Rule: one gate per operator.
Question 3
A Draw: X = NOT (A AND B)
B Gate 1: AND takes A and B
C Gate 2: NOT takes Gate 1
D Merge AND and NOT into NAND
Line D — The expression uses an AND operator and a NOT operator, so both gates must be drawn. Combining them into one NAND gate breaks the rule. It should say: Keep AND and NOT as two gates.
Question 4
A Draw: X = (A OR B) AND C
B Gate 1: AND takes A and B
C Gate 2: AND takes Gate 1, C
D Gates needed: 2
Line B — The bracket (A OR B) needs an OR gate for A and B, not an AND gate. It should say: Gate 1: OR takes A and B.
Question 5
A Draw: X = (NOT A) OR B
B Gate 1: NOT takes A
C Gate 2: OR takes A and B
D Gates needed: 2
Line C — The OR gate must take the output of the NOT gate, not A directly. Otherwise the NOT gate has been removed from the circuit. It should say: Gate 2: OR takes Gate 1 and B.

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