← IGCSE Computer Science Paper 2

Tracing one input combination through a circuit

Write the input values on the wires, then work gate by gate from left to right, writing each gate's output on its output wire until you reach the final output X.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 25

Understanding Tracing one input combination through a circuit in IGCSE Computer Science Paper 2

What it does: The OR gate is on the left and feeds the AND gate, so its output must be traced first before the AND gate can be worked out. After tracing every gate, the value on the last output wire is read as X. Here A AND B gives 1, then 1 OR 0 gives 1. OR outputs 1 when at least one input is 1. A is 1, so the output wire gets 1.

Common mistakes: The trace uses B as 0 in the AND gate (1 AND 0), so the inputs written on the wires must be A=1 B=0 C=1, not B=1. A NOT gate flips its input. NOT 0 is 1, so the output wire P must be 1, not 0.

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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
Where do you start when tracing one input combination through a circuit?
Write the final output X first, then work backwardsWrite the input values on the input wires on the left
Matches
A=1, B=0: A AND B = 1
↓
AND outputs 1 only when both inputs are 1. With inputs 1 and 0 the output on the wire should be 0, not 1.
Applying
Meanings
Term
trace a circuit
Meaning
Write the input values on the wires, then work gate by gate from left to right, writing each gate's output on its output wire until you reach the final output X.
Practice
A=1, B=0, C=0
Testing
Gaps
Trace a circuit from to right
Check Answer
Spots
1A=1 B=1 C=1
2P = A AND B = 1 AND 0 = 0

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Quick Questions

1. Where do you start when tracing one input combination through a circuit?
A. Write the input values on the input wires on the left ✓
B. Write the final output X first, then work backwards
Tracing starts by writing the 0 or 1 for each input (A, B, C) on its wire at the left. Then you work towards X.
2. Which direction do you work when tracing a circuit?
A. Right to left, from X back to the inputs
B. Left to right, from the inputs towards X ✓
Each gate needs its input values before you can find its output, so you work from the inputs on the left towards the output on the right.
3. A is 1 and B is 0 going into an AND gate. What do you write on the gate's output wire?
A. 0 ✓
B. 1
AND outputs 1 only when both inputs are 1. Here one input is 0, so the output wire gets 0.
4. A is 1 and B is 0 going into an OR gate. What do you write on the gate's output wire?
A. 0
B. 1 ✓
OR outputs 1 when at least one input is 1. A is 1, so the output wire gets 1.
5. A NOT gate has 1 on its input wire. What do you write on its output wire?
A. 0 ✓
B. 1
NOT flips its input, so 1 becomes 0 on the output wire.

Match the Pairs

A=1, B=0, A AND B = 0 → Write 1 on wire A and 0 on wire B, then the AND gate outputs 0 on its output wire
NOT gate: 0 in, 1 out → Write the gate's output on its output wire so the next gate to the right can use it as an input
Work through the gates from left to right, so a gate's inputs are known before you work out its output → (A OR B) AND C: do A OR B first, then AND with C
The final answer is the value written on the last wire, which is the output X → A=1, B=1, C=0 gives X = (A AND B) OR C = 1
A=1, B=0: A AND B = 1 → AND outputs 1 only when both inputs are 1. With inputs 1 and 0 the output on the wire should be 0, not 1.
Trace (A OR B) AND C: do AND first, then OR → The gates were traced in the wrong order. You must work left to right, so the OR gate is traced first and its output feeds the AND gate.

Key Term

trace a circuit
Write the input values on the wires, then work gate by gate from left to right, writing each gate's output on its output wire until you reach the final output X.

Fill in the Blanks

1. Trace a circuit from left to right
Hint: Type the direction you start from when working through the gates.
2. A = 1, B = 1 P = A NAND B = 1 NAND 1 = 0 X = NOT P = NOT 0 = 1
Hint: Type the value of the final output X after the NOT gate.
3. A = 1, B = 0, C = 1 P = A AND B = 1 AND 0 = 0 X = P OR C = 0 OR 1 = 1
Hint: Type the value this OR gate puts on the output wire.
4. A = 0, B = 1, P = A XOR B P = 0 XOR 1 = 1
Hint: Type the gate name used for P in the first line.
5. The wire after the last gate is output X
Hint: Type the letter that labels the final output.

Spot the Error

Question 1
A A=1 B=1 C=1
B P = A AND B = 1 AND 0 = 0
C X = P OR C = 0 OR 1 = 1
Line A — The trace uses B as 0 in the AND gate (1 AND 0), so the inputs written on the wires must be A=1 B=0 C=1, not B=1.
Question 2
A A=0 B=1 C=1
B P = NOT A = NOT 0 = 0
C Q = P AND B = 1 AND 1 = 1
D X = Q OR C = 1 OR 1 = 1
Line B — A NOT gate flips its input. NOT 0 is 1, so the output wire P must be 1, not 0.
Question 3
A A=1 B=1
B P = A NAND B = 1 NAND 1 = 0
C Q = NOT B = NOT 1 = 0
D X = P OR Q = 0 OR 0 = 1
Line D — An OR gate outputs 1 only if at least one input is 1. With both inputs 0, the final output X is 0, not 1.
Question 4
A A=1 B=0 C=0
B P = A OR B = 1 OR 0 = 1
C Q = P AND C = 1 AND 0 = 0
D X = P = 1
Line D — The final output X is the output of the last gate on the left-to-right path, which is Q. Q is 0, so the line should be X = Q = 0.
Question 5
A A=0 B=1 C=0
B P = A XOR B = 0 XOR 1 = 1
C Q = P NOR C = 1 NOR 0 = 1
D X = Q = 0
Line C — A NOR gate outputs 1 only when both inputs are 0. Here one input is 1, so the output is 0, not 1.

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