🎓 Learning Journey · Topic 1.4 · Cornerstone

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Bit, nibble, byte, and the 1024-step chain up to TiB. Seven stages from theory to mastery. Click any stage card to dive in — or continue where you left off.

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📚 Topic 1.4 · Data Representation · Trainer

Storage Units Trainer — bits to tebibytes

The full storage chain — bit, nibble, byte and each ×1024 unit above it — with the real calculations Cambridge expects.

📚 Book Notes

🎓 Learn

🎮 Activities

✎ Practice

📋 Exam

🔄 Review

🏆 Mastery

§1 · Topic overview

What is Topic 1.4?

Data storage is measured in a fixed chain of units. At the bottom is the bit (a single 0 or 1). Group 4 bits and you get a nibble. Group 8 bits and you get a byte. Above the byte, each unit is exactly 1024 times the one below: kibibyte, mebibyte, gibibyte, tebibyte.

Cambridge use the IEC binary prefixes — kibi, mebi, gibi, tebi (KiB, MiB, GiB, TiB) — because they're exact powers of 2. The SI decimal prefixes (kilo, mega, giga = 1000, 1,000,000, 1,000,000,000) are a common trap. In this lesson, always use 1024 for conversions.

This is the utility topic: every other data-representation lesson (text file sizes, image file sizes, sound file sizes) ends with a unit conversion. Master 1024 here and every downstream calculation gets easier.

§2 · Learning objectives

By the end of 1.4 you can…

Define bit, nibble, and byte, and state that 1 byte = 8 bits, 1 nibble = 4 bits
State the full chain: bit → nibble → byte → KiB → MiB → GiB → TiB
State that each level above the byte is exactly 1024× the one below
Convert up the chain (smaller → larger) by dividing by 1024
Convert down the chain (larger → smaller) by multiplying by 1024
Recognise the IEC binary prefixes: kibi (Ki), mebi (Mi), gibi (Gi), tebi (Ti)
Distinguish them from SI decimal prefixes (kilo/mega/giga = powers of 1000)
Calculate file/RAM sizes correctly — e.g. 4 GiB = 4 × 1024 = 4096 MiB, not 4000

§3 · Key terminology

Cambridge-approved terms

Term	Symbol	Definition
Bit	b	Binary digit — a single 0 or 1. The smallest unit of data.
Nibble	—	Group of 4 bits (half a byte). Maps to one hex digit.
Byte	B	Group of 8 bits. The standard smallest addressable unit.
Kibibyte	KiB	1024 bytes = 2¹⁰ bytes.
Mebibyte	MiB	1024 KiB = 2²⁰ bytes.
Gibibyte	GiB	1024 MiB = 2³⁰ bytes.
Tebibyte	TiB	1024 GiB = 2⁴⁰ bytes.
IEC prefix	Ki, Mi, Gi, Ti	Binary prefixes — always powers of 1024.

§4 · Core theory

The tables you must know cold

The full storage chain

Unit	Size in bits	Size in previous unit	Power of 2
Bit	1	—	2⁰
Nibble	4	4 bits	2²
Byte	8	2 nibbles / 8 bits	2³
Kibibyte (KiB)	8,192	1024 bytes	2¹⁰ bytes
Mebibyte (MiB)	8,388,608	1024 KiB	2²⁰ bytes
Gibibyte (GiB)	—	1024 MiB	2³⁰ bytes
Tebibyte (TiB)	—	1024 GiB	2⁴⁰ bytes

Conversion method — the direction rule

Direction	Operation	Example
Going UP (smaller → larger, e.g. bytes → KiB)	DIVIDE by 1024	8192 bytes ÷ 1024 = 8 KiB
Going DOWN (larger → smaller, e.g. GiB → MiB)	MULTIPLY by 1024	3 GiB × 1024 = 3072 MiB
Multi-step (bytes → MiB)	Do 1024 twice: ÷ 1024 then ÷ 1024	4,194,304 bytes ÷ 1024 = 4096 KiB ÷ 1024 = 4 MiB

SI vs IEC — the classic exam trap

SI decimal	Value	IEC binary	Value
Kilobyte (KB)	1000 bytes	Kibibyte (KiB)	1024 bytes
Megabyte (MB)	1,000,000	Mebibyte (MiB)	1,048,576
Gigabyte (GB)	1,000,000,000	Gibibyte (GiB)	1,073,741,824

For Cambridge, always use IEC (1024). Hard-disk manufacturers use SI (1000) to make drives sound larger — that's why a "1 TB" drive shows as about 931 GiB in your OS.

§5 · Worked examples

Watch each conversion done step by step

Worked example 1 · 4 GiB of RAM in mebibytes

A computer has 4 GiB of RAM. State this in mebibytes.

Going DOWN the chain (GiB → MiB), so MULTIPLY by 1024: 4 GiB × 1024 = 4096 MiB Answer: 4096 MiB NOT 4000 — that's the SI (decimal) approximation. Cambridge want the exact binary value.

Worked example 2 · 8192 bytes in kibibytes

Convert 8192 bytes to kibibytes.

Going UP the chain (bytes → KiB), so DIVIDE by 1024: 8192 ÷ 1024 = 8 KiB Answer: 8 KiB. Check: 8 × 1024 = 8192 ✓

Worked example 3 · 5 MiB in bytes

Convert 5 MiB to bytes.

Two steps DOWN the chain (MiB → KiB → bytes): Step 1: 5 MiB × 1024 = 5120 KiB Step 2: 5120 KiB × 1024 = 5,242,880 bytes Or in one step: 5 × 1024² = 5 × 1,048,576 = 5,242,880 bytes Answer: 5,242,880 bytes.

§6 · Common misconceptions

Traps that cost marks every session

Trap · Using 1000 instead of 1024

In Cambridge IGCSE, storage units use IEC binary prefixes (KiB, MiB, GiB, TiB) which are powers of 1024. Using 1000 gives the SI decimal answer — wrong for the exam. This is the #1 storage-units mistake every session.

Cited: 2024 examiner report — verbatim: "A wide range of incorrect answers were given involving some use of multiplication or division of 1024"

Trap · 4 GiB = 4000 MiB (should be 4096)

This exact mistake was called out in the 2024 examiner report. 4 GiB in mebibytes is 4 × 1024 = 4096. The 4000 answer treats "kibi/mebi/gibi" as if they were SI decimal — they aren't.

Cited: 2024 examiner report — verbatim: "Some candidates were able to state the amount of RAM in mebibytes. Some candidates gave the inaccurate answer of 4000."

Trap · Multiplying when you should divide (or vice versa)

Direction matters. Bytes → KiB means going UP the chain to a bigger unit, so the NUMBER gets smaller — DIVIDE. GiB → MiB means going DOWN to a smaller unit, so the NUMBER gets bigger — MULTIPLY.

Cited: recurring direction-confusion pattern

Trap · Missing the nibble in the chain

The full order is bit → nibble → byte → KiB → MiB → GiB → TiB. Students often omit nibble. A nibble is 4 bits — half a byte, or one hex digit.

Cited: recurring listing-order pattern

Trap · Confusing KB (kilobyte) with KiB (kibibyte)

KB (kilobyte, SI) = 1000 bytes. KiB (kibibyte, IEC) = 1024 bytes. Different symbols, different values. Cambridge use KiB/MiB/GiB/TiB — always the IEC binary versions. Read the question and use the right symbol.

Cited: recurring symbol-mix-up pattern

Trap · Doing single-step for multi-step conversion

To go from bytes to MiB, you cross TWO levels (bytes → KiB → MiB) so you divide by 1024 twice (or by 1024² = 1,048,576 once). One division alone gives KiB, not MiB.

Cited: recurring multi-step error

§7 · Cambridge exam focus

Mark-scheme templates

These are the exact phrasings Cambridge accept. Learn them.

"A byte contains 8 bits" — the fundamental relationship

"A nibble contains 4 bits (half a byte)" — nibble definition

"1 KiB = 1024 bytes / 1 MiB = 1024 KiB / 1 GiB = 1024 MiB / 1 TiB = 1024 GiB" — the chain

"To convert bytes to KiB, divide by 1024" — the up-direction

"To convert GiB to MiB, multiply by 1024" — the down-direction

"4 GiB = 4 × 1024 = 4096 MiB" — the exact answer expected

Never write: 1000 instead of 1024 · 4 GiB = 4000 MiB · KB = KiB (they're different)

§8 · Quick knowledge check

Check yourself — tap to reveal (0/6)

Answer these in your head, then tap to see the model answer. Aim for 5 or 6 right before moving on.

Q1 · How many bits in a byte? In a nibble?

Byte = 8 bits · Nibble = 4 bits. A nibble is half a byte, or one hex digit.

Q2 · State the storage chain in order.

bit → nibble → byte → KiB → MiB → GiB → TiB

Q3 · How many bytes in 1 KiB?

1024 bytes (that is 2¹⁰). NOT 1000 — that's KB, the SI decimal prefix.

Q4 · Convert 4 GiB to MiB.

4 × 1024 = 4096 MiB. NOT 4000 — that's the classic examiner-flagged mistake.

Q5 · Convert 8192 bytes to KiB.

8192 ÷ 1024 = 8 KiB. Going up the chain → divide.

Q6 · Convert 2 MiB to bytes.

Two steps down: 2 × 1024 = 2048 KiB, then 2048 × 1024 = 2,097,152 bytes. (Or 2 × 1024² directly.)

🚀 Ready for the rest
If you can answer 5 of the 6 knowledge checks above, you're ready to move on. Tap 🎓 Learn for the interactive conversion method, then 🎮 Activities for the Conversion Drill.

The storage unit chain

Think of Russian dolls — each unit fits inside the next, always multiplied by the same number.

Bit

1 digit

×4→

Nibble

4 bits

×2→

Byte

8 bits

×1024→

KiB

Kibibyte

×1024→

MiB

Mebibyte

×1024→

GiB

Gibibyte

×1024→

TiB

Tebibyte

×1024→

PiB

Pebibyte

×1024→

EiB

Exbibyte

⚠ The golden rule: Binary prefixes always use 1024, never 1000. Denary prefixes (KB, MB, GB using 1000) are not on the Cambridge syllabus. (Mar 2023, Jun 2024)

The bottom three — know these cold

Unit	Size	Exam trap
Bit	1 binary digit	The smallest unit — not nibble (Nov 2024)
Nibble	4 bits	Don't confuse with byte. 4 bits, not 8 (Jun 2025)
Byte	8 bits = 2 nibbles	2 nibbles, NOT 4 or 8 (Nov 2024, Jun 2025)

Converting — the method

Going UP (smaller → larger)

Divide by 1024 at each level.

512 KiB → MiB
512 ÷ 1024 = 0.5 MiB

Going DOWN (larger → smaller)

Multiply by 1024 at each level.

4 GiB → MiB
4 × 1024 = 4096 MiB

⚠ Trap: When converting one level, multiply or divide by 1024 once. Don't multiply by 1024×1024 for a single step. (Jun 2025)

Quick check

How many nibbles are in 1 byte?

Activity 1 — Conversion Drill

Press New Question.

Activity 2 — Spot the Mistake

Press New Question.

Activity 3 — Unit Identifier

Press New Question.

Adaptive practice

Press New Question.

Cambridge-style questions

Press New Question.

Review quiz

Press New.

Exam traps

⚠ 1: Always 1024, never 1000. Denary prefixes not on syllabus. (Mar 2023, Jun 2024)

⚠ 2: 1 byte = 2 nibbles. NOT 4 or 8. (Nov 2024, Jun 2025)

⚠ 3: The smallest unit is bit, not nibble. (Nov 2024)

⚠ 4: A nibble is 4 bits. Don't say byte when you mean nibble. (Jun 2025)

⚠ 5: One level = ×1024 or ÷1024. Don't multiply by 1024×1024 for a single step. (Jun 2025)

Memory triggers

🧠 "Russian dolls × 1024"

Each unit contains exactly 1024 of the unit below it. Always. No exceptions.

🧠 "2 nibbles, not 4, not 8"

1 nibble = 4 bits. 1 byte = 8 bits. 8 ÷ 4 = 2 nibbles per byte. Students mix these up constantly.

🧠 "KiB MiB GiB TiB PiB EiB"

Say it rhythmically: Kib-Mib-Gib-Tib-Pib-Eib. The order never changes.

Mastery Map

Checkpoints

[ ] Bit is the smallest unit

[ ] Nibble = 4 bits

[ ] Byte = 8 bits = 2 nibbles

[ ] Name all 6 binary prefixes in order

[ ] Always use 1024

[ ] Convert up (÷1024)

[ ] Convert down (×1024)

[ ] Multi-step conversions

[ ] Denary prefixes not on syllabus

[ ] Cambridge exam confidence