From bits and bytes to full 8-bit denary/binary fluency. Seven stages from theory to mastery. Click any stage card to dive in — or continue where you left off.
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Master the binary number system, 8-bit place values, and conversions between binary and denary. The starting stone for everything else in Cambridge IGCSE 0478.
Every letter, number, image, sound, and video on a computer is stored the same way: as bits — patterns of 0s and 1s. Before you can understand how a computer stores a photograph or plays a song, you have to understand how it stores a single number. That's what Topic 1.1A is about.
By the end of this lesson you'll be able to convert between denary (the numbers humans use) and binary (the numbers computers use), and you'll know why computers use binary in the first place. It's foundational — every other topic in the syllabus assumes you know this.
| Term | Definition |
|---|---|
| Bit | A single binary digit — either 0 or 1. The smallest unit of data. |
| Binary | A base-2 number system using only the digits 0 and 1. |
| Denary | A base-10 number system using digits 0–9. Also called decimal. |
| Nibble | A group of 4 bits. Half a byte. Equal to one hexadecimal digit. |
| Byte | A group of 8 bits (2 nibbles). |
| Base | The number of unique digits in a number system (binary=2, denary=10, hex=16). |
| Place value | The value of each column in a number. In 8-bit binary: 128, 64, 32, 16, 8, 4, 2, 1. |
| Most significant bit (MSB) | The leftmost bit — the highest place value (128 in 8-bit). |
| Least significant bit (LSB) | The rightmost bit — the lowest place value (1 in 8-bit). |
| Logic gate | An electronic switch inside a computer with two states: on (1) or off (0). Why computers use binary. |
| Unit | Size | Example |
|---|---|---|
| Bit | 1 binary digit | 0 or 1 |
| Nibble | 4 bits | 1010 |
| Byte | 8 bits (2 nibbles) | 10101010 |
| Column | MSB → | ← LSB | ||||||
|---|---|---|---|---|---|---|---|---|
| Place value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| Power of 2 | 2⁷ | 2⁶ | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰ |
| System | Base | Digits allowed | Multiplier per column |
|---|---|---|---|
| Binary | 2 | 0, 1 | ×2 |
| Denary | 10 | 0–9 | ×10 |
| Hexadecimal | 16 | 0–9, A–F | ×16 |
Convert the 8-bit binary number 10101000 to denary.
Convert the denary number 150 to 8-bit binary.
Cambridge award marks for working even when the final answer is wrong. On a 2-mark conversion question you get 1 mark for correct method and 1 mark for correct answer. So always write down the place values and show subtractions.
Students write "smallest = 1" thinking bits can't all be 0. But 00000000 is a valid 8-bit number — and it equals 0. Range: 0 to 255, inclusive.
Examiners flag this as a vague answer. The mark-winning answer references switches or logic gates that can only be in two states: on (1) or off (0). That's the physical reason.
Cited: 2024 examiner report — verbatim "vague statements such as 'a computer can only understand binary'"1 nibble = 4 bits. 1 byte = 8 bits. So 1 byte = 2 nibbles, not 8. Students confuse the multiplication.
Cited: 2024 Nov examiner reportIf the question asks for an 8-bit binary number, you must write all 8 digits — including leading zeros. Writing 1101 when the question wanted 00001101 loses the mark.
Cambridge award marks per step. Correct final answer with no working = fewer marks than correct working with a small arithmetic slip. Always write down the place values or subtractions.
Cited: 2024 examiner report — "Some candidates had appropriate working, but then…"The bit is the smallest unit of data — a single 0 or 1. A group of 4 bits is a nibble. Students sometimes call any small unit a "bit" incorrectly.
Cited: 2024 Nov examiner reportThese are the exact phrasings Cambridge accept. Learn them.
Answer these in your head, then tap to see the model answer. You should get 5 or 6 correct before moving to Learn.
A switch has exactly two states: ON and OFF. A computer is billions of tiny electronic switches. Each switch stores one bit — either 1 (on) or 0 (off).
Computers are built from logic gates — tiny circuits that only have two states. Binary maps directly to these two states. This is the exam answer.
Never write "the computer only understands binary" — this is too vague. You must mention switches or gates with two states (on/off).
"Computers use binary because they only allow 1s and 0s to be entered" is wrong. The reason is the two-state nature of switches and gates.
Cited: 2024 examiner report — verbatimThe number system humans use daily. Uses digits 0–9. Place values: ones, tens, hundreds, thousands. Each column is ×10.
The number system computers use. Uses only digits 0 and 1. Place values: 1, 2, 4, 8, 16, 32, 64, 128. Each column is ×2.
| Unit | Size | Example |
|---|---|---|
| Bit | 1 binary digit | 0 or 1 |
| Nibble | 4 bits | 1010 |
| Byte | 8 bits (2 nibbles) | 10101010 |
The smallest unit of data is a bit, not a nibble. A byte contains 2 nibbles, not 8.
Cited: 2024 Nov + 2025 examiner reportsClick each bit to toggle it on or off. Watch how the denary value changes. This is the mental model that gets you through every conversion question.
Write the place values above each bit. Add up every place value where the bit is 1.
Start from 128. If the place value fits, write 1 and subtract. If not, write 0. Repeat for each place value.
Smallest = 00000000 = 0. Largest = 11111111 = 255. Confirmed in 2025 F/M P12 Q1 fill-in-blank.
Six common command-word shapes you'll see in Paper 1.
Why do computers use binary?
A denary number appears below. Toggle the correct bits to build it in binary.
Stretch: can you get 5 correct in a row without clearing between attempts?
Convert as many numbers as you can. Difficulty increases every 3 correct answers.
Press Start to begin.
Stretch: once you reach level 3 (0–255 range), can you complete 10 without a mistake?
Which statement contains a mistake that examiners have flagged?
Press New Question.
Stretch: after you get it right, explain out loud why the wrong statement is wrong — using the exam-answer phrasing.
Type the missing values. Aim for 3 in a row without error.
Press New Question.
Stretch: after 3 correct, try writing out the full 8-bit place value list from memory in the notepad.
Answer as many binary-related questions as you can in 60 seconds. Ideal warm-up before Practice or Exam.
Press Start Sprint to begin.
Stretch: beat your personal best twice in a session to earn the Sprint mastery tick.
Weak skills come round twice as often; strong ones five times less. No question repeats immediately. 18+ questions across 9 skills.
Press New Question.
12 questions in Cambridge Paper 1 style. Every question cites its source. Write your answer, then click Mark for keyword-based scoring.
Press New Question to begin.
Press New Question.
Every trap below is drawn from a real Cambridge examiner report or a recurring pattern flagged across multiple sessions.
00000000 = 0 is a valid 8-bit number. Range is 0 to 255 inclusive.
Vague answer. Must reference switches or logic gates with two states (on/off).
Cited: 2024 examiner report — "vague statements such as 'a computer can only understand binary'"1 nibble = 4 bits. 1 byte = 8 bits = 2 nibbles.
Cited: 2024 Nov examiner reportIf the question asks for an 8-bit binary number, write all 8 digits — including leading zeros.
Cited: recurring across 2023–2025Cambridge award marks per step. Correct answer with no working scores fewer marks than correct working with an arithmetic slip.
Cited: 2024 examiner report — "Some candidates had appropriate working, but then…"The bit is the smallest unit of data — a single 0 or 1. Not 4 bits, not "a small piece of data".
Cited: 2024 Nov examiner reportSome students convert binary → denary, do the sum in denary, then convert back. The question wants the calculation done in the target system. Doing it via denary can lose marks — and creates arithmetic errors.
Cited: 2023 examiner report — "Some candidates converted the values to denary, added the values and converted the answer back to binary. Candidates should note that this is not [the required method]"Binary = base 2. Denary = base 10. Hexadecimal = base 16. Students sometimes swap them — losing a fill-blank mark that's very easy to secure.
Cited: 2025 F/M Paper 12 Q1 fill-blank format"Denary" means "base 10 whole numbers" — not "numbers with a decimal point". A denary number can be 45, 100, 255. Don't overcomplicate the term.
Cited: recurring pattern across mock papersStart from 1 on the right and keep doubling: 1, 2, 4, 8, 16, 32, 64, 128. That's all 8-bit place values in order — read right-to-left.
11111111 = 128+64+32+16+8+4+2+1 = 255. All bits on = maximum. All bits off = 0 (minimum). Range is 0 to 255.
Bit is 1 bit. Nibble is 4 bits (×4). Byte is 8 bits (×2). So 1 → 4 → 8. And 1 byte = 2 nibbles.
When asked "why binary?" — answer switches or gates with two states (on/off). Never "the computer understands it" or "only 1s and 0s".
Every conversion is worth method marks. Even if your arithmetic slips, showing the place-value subtraction earns partial marks. No working = all or nothing.
If Cambridge specify 8-bit, your answer must have exactly 8 digits. Pad with leading zeros. 01101 is wrong when they wanted 00001101.
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Ten items. Tap each once you're confident. When all 10 are ticked, 1.1A is mastered.
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