CAIE 9618 · Paper 1 · Topic 1.1.1

Number
Systems

Binary · Denary · Hexadecimal · Units of Storage

CSZone Cambridge International AS & A Level Computer Science 9618

Learning Objectives

By the end of this video you will be able to...

Convert numbers between binary, denary, and hexadecimal

Explain why computers use the binary number system

State the units of storage: bit, nibble, byte, KB, MB, GB, TB

Answer Cambridge 9618 exam questions on number bases with confidence

Why Binary?

Computers Use Base 2

"All data in a computer is ultimately stored as binary — sequences of 0s and 1s — because electronic circuits have two stable states: ON and OFF."

BINARY (BASE 2)

Only digits: 0 and 1

Each digit called a bit (binary digit)

Represented by voltage: HIGH = 1, LOW = 0

DENARY (BASE 10)

Digits: 0 – 9

The number system humans use naturally

Each column is a power of 10

Binary Place Values

Converting Binary → Denary

8-BIT PLACE VALUE TABLE

128	64	32	16	8	4	2	1
1	0	1	1	0	1	0	1

128 + 32 + 16 + 4 + 1 = 181 ∴ 10110101₂ = 181₁₀

Add the place values where the bit is 1 — ignore where the bit is 0

Each column is double the previous: 1, 2, 4, 8, 16, 32, 64, 128...

Conversion Method

Denary → Binary: Two Methods

METHOD 1: PLACE VALUES

Convert 219 to binary:
219 ≥ 128? YES → 1, remainder 91
91 ≥ 64? YES → 1, remainder 27
27 ≥ 32? NO → 0
27 ≥ 16? YES → 1, remainder 11
11 ≥ 8? YES → 1, remainder 3
3 ≥ 4? NO → 0, 3 ≥ 2? YES → 1, r1
1 ≥ 1? YES → 1
Answer: 11011011

METHOD 2: REPEATED DIVISION BY 2

219 ÷ 2 = 109 r 1
109 ÷ 2 = 54 r 1
54 ÷ 2 = 27 r 0
27 ÷ 2 = 13 r 1
13 ÷ 2 = 6 r 1
6 ÷ 2 = 3 r 0
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1 ← Read up
Answer: 11011011

Hexadecimal (Base 16)

Why Use Hexadecimal?

Hexadecimal provides a compact, human-readable representation of binary.
Every group of 4 binary bits maps directly to one hex digit.

Denary	Binary	Hex	Denary	Binary	Hex
0	0000	0	8	1000	8
4	0100	4	10	1010	A
7	0111	7	15	1111	F

💡 Hex uses A=10, B=11, C=12, D=13, E=14, F=15 — remember this for the exam

Hex Conversion

Binary ↔ Hexadecimal

BINARY → HEX

Group bits in fours from the right:
1011 0101
1011 = 11 = B
0101 = 5 = 5
Answer: B5_₁₆

HEX → DENARY

Convert 2F₁₆ to denary:
2 × 16¹ = 2 × 16 = 32
F × 16⁰ = 15 × 1 = 15
Answer: 32 + 15 = 47

📝 In the 9618 exam, hex is used to represent memory addresses, machine code, and colour codes (RGB)

Units of Storage

From Bits to Terabytes

Unit	Symbol	Equivalent	Approx. Size
Bit	b	1 binary digit (0 or 1)	Single on/off value
Nibble	—	4 bits	One hex digit
Byte	B	8 bits	One character (ASCII)
Kilobyte	KB	1,000 bytes	Short text document
Megabyte	MB	1,000 KB	MP3 song (~3 min)
Gigabyte	GB	1,000 MB	~200 photos
Terabyte	TB	1,000 GB	Home hard drive

Cambridge 9618 uses SI prefixes: 1 KB = 10³ bytes · 1 MB = 10⁶ bytes · 1 GB = 10⁹ bytes · 1 TB = 10¹² bytes

Exam Practice

Cambridge-style questions — attempt before revealing

Question 1

Convert the binary number 10110101 to denary. Show your working.

2 marks

✓ MARK SCHEME

1 mark

Working shown: 128 + 32 + 16 + 4 + 1 or equivalent place values identified

1 mark

Correct answer: 181 (award if working correct but arithmetic slip)

⚠ Always show the place values — 1 mark is for working, not just the answer

Exam Practice

Question 2

A file is described as having a size of 2.5 MB. How many bytes is this? Give your answer using Cambridge 9618 SI prefix notation.

1 mark

✓ MARK SCHEME

1 mark

2.5 × 10⁶ = 2,500,000 bytes (2.5 million bytes)

9618 uses SI: 1 MB = 1,000,000 bytes. Not 1,048,576 (that is 1 MiB — mebibyte)

Question 3

Convert the hexadecimal number A3 to denary.

2 marks

✓ MARK SCHEME

1 mark

A = 10, so: (10 × 16) + (3 × 1) shown

1 mark

Answer: 163

Common Mistakes

Don't lose easy marks

1

Confusing KB and KiB — Cambridge 9618 uses SI prefixes: 1 KB = 1,000 bytes, NOT 1,024. Writing 1,024 for 1 KB will lose marks in calculation questions.

2

Forgetting A=10 through F=15 in hexadecimal — a common slip is treating A as 11 or F as 14. Memorise: A B C D E F = 10 11 12 13 14 15.

3

Not showing working in conversion questions — "2 marks" almost always means 1 mark for the method/working and 1 mark for the answer. Writing just the final answer risks losing half the marks.

4

Grouping hex from the left instead of the right — always split binary into nibbles starting from the rightmost bit, padding with leading zeros if necessary.

Topic Summary — 1.1.1

What You Need to Know

NUMBER SYSTEMS

Binary (base 2) — digits 0 and 1
Denary (base 10) — digits 0 to 9
Hexadecimal (base 16) — digits 0–9, A–F
4 binary bits = 1 hex digit (nibble)

CONVERSIONS

Binary→Denary: add place values where bit=1
Denary→Binary: subtract largest place values
Binary→Hex: group in nibbles from right
Hex→Denary: multiply each digit by 16^n

STORAGE UNITS (SI)

1 bit = one binary digit
1 byte = 8 bits
1 KB = 1,000 bytes (10³)
1 MB = 1,000,000 bytes (10⁶)
1 GB = 10⁹ bytes · 1 TB = 10¹² bytes

CSZone

Next Video

1.1.2

Binary Arithmetic & Two's Complement

Addition · Overflow · Signed Integers

Head to CSZone.co.uk for the complete worksheet, quiz, and interactive tools

NumberSystems

By the end of this video you will be able to...

Computers Use Base 2

Converting Binary → Denary

Denary → Binary: Two Methods

Why Use Hexadecimal?

Binary ↔ Hexadecimal

From Bits to Terabytes

Cambridge-style questions — attempt before revealing

Don't lose easy marks

What You Need to Know

Next Video

Number
Systems