7.2b Trace Tables & Desk Checking — Cambridge IGCSE CS 0478

What is a Trace Table?

A trace table (also called a dry run or desk check) is a manual method of testing an algorithm by stepping through it line by line and recording the value of each variable at every step.

You create columns for each variable, and one or more columns for any output. For each step of the algorithm, you fill in the current value of every variable that changes.

Why are trace tables used? They are used to: (1) check that an algorithm produces the correct output, (2) identify errors (bugs) in an algorithm, (3) understand what an existing algorithm does. These are key exam marks.

How to Complete a Trace Table

Follow these steps:

Create one column per variable (and one for output)
Work through the algorithm line by line
Only write a new value in a cell when that variable changes
Leave cells blank when the variable does not change
Write output values in the OUTPUT column when an OUTPUT statement is reached

Example 1 — Simple algorithm

count ← 0
total ← 0
FOR i ← 1 TO 5
    total ← total + i
    count ← count + 1
NEXT i
OUTPUT total
OUTPUT count

Trace table:

i	total	count	OUTPUT
—	0	0
1	1	1
2	3	2
3	6	3
4	10	4
5	15	5
			15
			5

Example 2 — Conditional with a WHILE loop

x ← 10
y ← 1
WHILE x > 0 DO
    y ← y * 2
    x ← x - 3
ENDWHILE
OUTPUT y

Trace table:

x	y	OUTPUT
10	1
7	2
4	4
1	8
-2	16
(x = -2, condition x > 0 is FALSE, loop ends)		16

Identifying Errors with Trace Tables

A trace table helps find three types of errors:

Error Type	Description	Example
Logic error	Algorithm runs but gives wrong result	Using < instead of <=, causing loop to miss the last value
Infinite loop	Loop condition never becomes false	WHILE count < 10 but count is never incremented
Off-by-one error	Loop runs one too many or too few times	FOR i ← 1 TO 9 when you need 1 TO 10

⚠️ Common Mistakes in Trace Table Questions

Writing every value in every cell — only write when a variable CHANGES
Getting the loop termination wrong — always check: does the condition use < or <= ?
Forgetting the initialisation row (the very first values before any loop)
Not knowing whether a WHILE loop can run 0 times (yes it can) — check the starting condition

▶

Video coming soon

Click slide or press arrow keys to navigate

✍️

Worksheet — Trace Tables

4 questions · 10 marks

Q1State two reasons why a programmer might use a trace table. [2]

✅ Mark scheme

Any two: to check an algorithm produces the correct output [1]; to find/identify errors (bugs) in an algorithm [1]; to understand what an existing algorithm does [1]

Q2Complete a trace table for this algorithm and state the output:
a ← 2
b ← 1
FOR i ← 1 TO 4
b ← b + a
a ← a * 2
NEXT i
OUTPUT b [4]

✅ Mark scheme

i=1: b=3, a=4 [1]; i=2: b=7, a=8 [1]; i=3: b=15, a=16 [1]; i=4: b=31, a=32 [1]; OUTPUT = 31

Q3What type of error would cause a loop to never terminate? What does it mean for the program? [2]

✅ Mark scheme

A logic error / infinite loop [1]; the program will run forever (crash or become unresponsive / need to be terminated) [1]

Q4Describe what is meant by an 'off-by-one' error and give an example. [2]

✅ Mark scheme

An error where a loop runs one too many or one too few times [1]; e.g., writing FOR i ← 1 TO 9 when the loop should go from 1 to 10 [1]

Quiz — Trace Tables

Q 1 of 7

Score

/ 7

Click to reveal

Term	Definition

🔒

Pro Content

Upgrade to access all lessons.

£7.99/month

or £59/year

Subscribe now →

What is a Trace Table?

How to Complete a Trace Table

Example 1 — Simple algorithm

Example 2 — Conditional with a WHILE loop

Identifying Errors with Trace Tables

Worksheet — Trace Tables

Mini Test — Trace Tables