DSE ICT: Data Representation Prep Guide (for tutors) | Binary and hexadecimal, character encoding, file size and bandwidth

2026-11-02

Tutor lesson-prep guides · Secondary ICT

Students can say that computers use binary, then freeze when 0x2F has to become binary or when they must size a 1000-character Chinese file. This lesson runs one chain: bit, byte, character, pixel, file, transfer time, all measured with the same ruler.

Objectives — Students can: (1) convert between binary, decimal and hexadecimal and explain that one hexadecimal digit is four bits; (2) size a text file from the byte count per character in ASCII and UTF-8; (3) size an uncompressed image from resolution times bit depth, extend it to video by frames and seconds, then get transfer time from bandwidth.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Indices	What is 2 to the power 10	1024
Units	How many MB in a GB	1024 MB
Fractions	Three bytes out of 24 bits as a fraction	One eighth

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Bits and bytes	Eight bits make one byte	State that 1 KiB is 1024 bytes
8-20 min	Binary and hexadecimal	Four bits per hex digit	Write 0x2F as 101111 and 47
20-30 min	Character encoding	Bytes per character in ASCII and UTF-8	Get 3,000 bytes for 1000 Chinese characters
30-44 min	Pixels and bit depth	Resolution times bit depth	One frame is 5.93 MiB
44-54 min	Files, video and bandwidth	Bits and bytes differ by eight	60 s of video is 10.43 GiB; 12.5 MB/s at 100 Mbit/s
54-60 min	Exit check	Three questions marked on the spot	All three right

03 Teaching script (read it out)

Scene 1: Hexadecimal is just another way to write the same bits

A bit holds 0 or 1; eight bits make a byte, which covers 256 values from 0 to 255.
Hexadecimal is shorthand for people: every four bits become one hex digit, so a byte is always two hex digits.
Example: in 0x2F, the 2 is 0010 and the F is 1111, giving 101111, which is 47 in decimal.
Binary to decimal means adding powers of two: 32 plus 8 plus 4 plus 2 plus 1 equals 47.
Decimal to binary means repeated division by two, keeping remainders from the bottom up.
A 4 GiB drive is 4 times 1024 cubed, that is 4,294,967,296 bytes or 4,096 MiB; a vendor writing 4 GB in decimal gives a different number, about 7 per cent more.

Ask the class: how many hex digits are in one byte (two).

Scene 2: Character encoding decides how many bytes one character takes

ASCII uses seven meaningful bits but still occupies one byte: A is 65 and a is 97, a difference of 32, so letter case is one bit apart.
UTF-8 is variable length: one byte for English letters, three bytes for common Chinese characters.
So a 1000-character Chinese text file is 1000 times 3, that is 3,000 bytes, about 0.0 KiB; the same 1000 English letters take only 1000 bytes.
Pixels also need bits: 24-bit true colour gives 8 bits per channel, 256 levels each, so 16,777,216 colours in total.
Colour count and file size are therefore different questions: bit depth fixes the colours, and size also needs the pixel count.

Ask the class: how many bytes does one Chinese character take in UTF-8 (three).

Scene 3: From pixel to file to transfer time, it is all multiplication

For a 1920 by 1080 uncompressed 24-bit image: 1920 times 1080 times 3 equals 6,220,800 bytes, that is 5.93 MiB.
At 30 frames per second for 60 seconds: multiply by 30 then 60, giving 11,197,440,000 bytes, that is 10.43 GiB, which is why video must be compressed.
A 5 MiB MP3 at 128 kbit/s lasts 5 times 1024 times 1024 times 8 divided by 128000, which is 5 min 27.7 s.
A 100 Mbit/s link gives 12.5 MB/s after dividing by eight, so 5 MiB takes about 0.4 s; mixing bits and bytes is the most common lost mark here.

Ask the class: how many MB per second is 100 Mbit/s (12.5).

04 Question types and worked steps

Type	Example	Steps	Answer
Conversion	Binary and hexadecimal	Group in fours, look up each group, then join	101111 is 47
Calculation	Text file size	Characters times bytes per character	3,000 bytes
Calculation	Uncompressed image size	Width times height times bit depth over eight	5.93 MiB
Calculation	Transfer time	Bytes times eight over bit rate	100 Mbit/s is 12.5 MB/s

Sanity check (teach this): One hex digit is four bits and one byte is eight, so a byte is always two hex digits.
Capital B means bytes and lower-case b means bits; one B is eight b, so getting the direction wrong changes the answer by eight times.
KiB is 1024 and KB is 1000; if a question says GB, state which definition you used.
A compressed file is always smaller than resolution times bit depth, never larger.

05 Independent practice (3 questions)

Question	Answer	What to watch
Convert 0x2F to binary and decimal	101111 and 47	Four bits per hex digit, then powers of two
Size of a 1000-character Chinese text file in UTF-8	3,000 bytes	Three bytes per character
1920 by 1080 image at 24-bit colour	5.93 MiB	Width times height times three, then divide by 1024 squared

06 Common mistakes and what to say

Mistake	Student writes	Say this
Treating one hex digit as one byte	0x2F is two bytes	A byte is eight bits and a hex digit is four, so two digits make one byte.
Mixing bits and bytes	100 Mbps means 100 MB per second	Mbps is bits, so divide by eight: 12.5 MB per second.
Confusing colour count with file size	It is 24-bit so the file is huge	Bit depth fixes the colour count; size also needs the pixel count.
Mixing 1024 and 1000	4 GB means 4000 MB	Check the definition: 4 GiB is 4,096 MiB, while the decimal reading gives 4000 MB.

07 Homework (paper, section and question numbers)

Practice: binary, hexadecimal and character encoding — Write the unit before the number
Practice: image, video and bandwidth estimates — Do one frame first, then multiply
All prep guides — Compare the ten sections

08 Exit check (last 5 minutes)

Question	Answer	Decision
Binary value of 0x2F	101111	All three right: move to data organisation
UTF-8 size of 1000 Chinese characters	3,000 bytes	One wrong: redo the encoding table
MB per second at 100 Mbit/s	12.5 MB/s	Two or more wrong: return to act three

09 Tutor FAQ

Do students memorise the ASCII table?

Three anchors are enough: A is 65, a is 97 and 0 is 48; the rest follow by adding.

Why teach video size?

It practises multiplication and unit conversion, and it explains why compression exists.

Is hexadecimal really used?

Colour codes, memory addresses and MAC addresses all use it, so students stop fearing it once they have seen it.

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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.