DSE ICT | Data Representation and File Size Tutor Prep Guide

DSE ICT | Data Representation and File Size Tutor Prep Guide | Binary, hex, pixels and sampling

2026-11-01

Tutor lesson-prep guides · Secondary ICT

Students can say that computers use binary, but ask for the size of an 800 by 600 image at 24 bits and the multiplication collapses. This lesson turns bits, bytes and megabytes into one fixed pipeline that also covers sound and text.

Objectives — Students can: convert between binary, denary and hexadecimal; compute image size as pixel count times bit depth divided by eight; compute sound size as sampling rate times bit depth times channels times seconds, and use a compression ratio to get the compressed size.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Multiplication	How many pixels in 800 by 600	480,000
Units	How many bits in one byte	Eight
Binary range	How many values can four bits hold	16, from 0 to 15

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0 to 8 min	Bits and units	Bit, byte, kilobyte, megabyte, all through dividing by eight	States 1 byte is 8 bits
8 to 20 min	Base conversion	Binary, denary, hex, one hex digit per nibble	202 is 0xCA
20 to 34 min	Image size	Pixels times bit depth divided by eight	1.37 MB
34 to 46 min	Sound size	Rate times depth times channels times seconds divided by eight	30.28 MB
46 to 56 min	Compression traps	Ratio, lossy versus lossless, 1000 versus 1024	5 to 1 gives 6.06 MB
56 to 60 min	Exit check	Three questions collected and marked	Independent

03 Teaching script (read it out)

Scene 1: Bits to megabytes: one divide by eight pipeline

Inside the computer everything is a zero or a one. One digit is a bit and eight bits make a byte. Every question about file size starts the same way: count the bits, divide by eight to get bytes, then step up with 1024 to kilobytes and megabytes.
Example: 2,000 English letters at eight bits each is 16,000 bits, which is 2,000 bytes, about 2.0 kilobytes. The same 2,000 Chinese characters in UTF-8 take three bytes each, so 6,000 bytes.

Ask the student why a drive sold as one terabyte shows 931 gigabytes (the maker counts 1000, the system counts 1024).

Scene 2: Images: pixels times bit depth divided by eight

A bitmap is a grid of pixels. Bit depth says how many bits describe each pixel, so 24 bits means eight bits for red, green and blue, which is three bytes per pixel.
An 800 by 600 image at 24 bits therefore holds 800 times 600 equals 480,000 pixels, times three bytes equals 1,440,000 bytes, which is 1,406.25 kilobytes or 1.37 megabytes.
Compare a 600 by 400 greyscale image at 8 bits: 600 times 400 times one byte equals 240,000 bytes, only 234.4 kilobytes.

Ask the student to compute the same image at 16 bits, two bytes per pixel, which gives 960,000 bytes.

Scene 3: Sound: rate times depth times channels times seconds

Sound is a continuous wave, so digitising needs two decisions: how often to measure each second (sampling rate) and how many bits to store each measurement (bit depth). CD quality is 44,100 hertz, 16 bits, in stereo.
Three minutes is 180 seconds, so the file is 44,100 times 2 times 2 times 180 equals 31,752,000 bytes, about 30.28 megabytes. At 5 to 1 it shrinks to about 6.06 megabytes.
Plain text of the same duration is only a few kilobytes, because sound is sampled tens of thousands of times a second while text adds a few characters a second.

Reminder: MP3 is lossy, so detail is gone for good, while ZIP is lossless and restores the original exactly.

04 Question types and worked steps

Type	Example	Steps	Answer
Convert	Denary 202 to hexadecimal	Divide by 16 and keep the remainders	0xCA, since 12 is C and 10 is A
Calculate	800 by 600 image at 24 bits	Pixels times three bytes	1,440,000 bytes, about 1.37 MB
Calculate	Three minutes at 44.1 kilohertz, 16 bit stereo	Rate times two times two times 180	30.28 MB
Explain	Why sound files dwarf text files of the same length	Samples per second versus characters per second	Several orders of magnitude

Sanity check (teach this): An 800 by 600 image at 24 bits must land between one and two megabytes, so 1,400 megabytes means the divide by eight was skipped. One minute of CD audio is about 10 megabytes, so three minutes near 30 megabytes is right and anything in gigabytes jumped a unit. Hexadecimal digits only run from 0 to 9 and A to F, so a G means the conversion failed.

05 Independent practice (3 questions)

Question	Answer	What to watch
600 by 400 greyscale at 8 bits	240,000 bytes, about 234.4 KB	Pixels times one byte
Ten seconds at 8,000 hertz, 8 bit mono	80,000 bytes, about 78.1 KB	Rate times one times one times ten
Hexadecimal 0x2F to denary	47	Two times 16 plus 15

06 Common mistakes and what to say

Mistake	Student writes	Say this
Forgetting to divide by eight	Answers 1,440,000 kilobytes	You counted bits; a byte is eight bits, so divide by eight.
Using 1000 for a kilobyte	Treats a megabyte as a million bytes	Computers step by 1024, not by a thousand.
Reading bit depth as the whole image	Multiplies 24 by the pixels and stops	24 is bits per pixel, not bytes for the image.
Dropping the channel count	Treats stereo as mono	Stereo means two channels, so multiply by two.

07 Homework (paper, section and question numbers)

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Prep guide hub — Every subject

08 Exit check (last 5 minutes)

Question	Answer	Decision
Size of an 800 by 600 image at 24 bits	1.37 MB	All three right: move to sound
Size of three minutes of CD quality stereo	30.28 MB	One wrong: reteach the divide by eight
How many bits in one byte	Eight	Two wrong: restart scene one

09 Tutor FAQ

Why do images count 1024 while drives count 1000?

The computer works in binary where 1024 is two to the tenth power, while drive makers use decimal thousands for tidier advertising.

Is a higher sampling rate always better?

It tracks the original more closely, but the file grows in proportion, so the rate is chosen for the purpose.

What does a compression ratio of 5 to 1 mean?

Five bytes of data become one, so the file is one fifth of its original size.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.