IB Computer Science HL · Year 2 · Lesson 31

Binary/hex and binary data representation

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Paper 150 minutesA1.2.1 · A1.2.2
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Today’s targets

What you need to be able to do

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  • DescribeThe principal methods of representing data
  • ExplainHow binary is used to store data
A1.2.1A1.2.2
Paper 1 lensMatch the depth of every response to the command term. Previously learned content can move quickly, but retrieval must still be accurate.
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Retrieve

Rapid Recall Deck

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Say the answer aloud before flipping. Mark secure knowledge quickly and spend time on the gaps.

  • What digits are used in binary and hexadecimal?: Binary uses 0 and 1; hexadecimal uses 0–9 and A–F to represent values 0–15.
  • How many binary bits correspond to one hexadecimal digit?: Four bits (one nibble).
  • Why is hexadecimal convenient when working with binary data?: Each hex digit maps exactly to four bits, so long binary values can be written more compactly without losing the bit pattern.
  • Why can computers represent many data types using binary?: At the hardware level data is encoded as patterns of two states/bits; agreed encoding schemes give those patterns meaning.
  • How are non-numeric data such as text, images, audio, and video stored?: They are converted into binary according to an encoding or representation scheme, such as character codes, pixel values, or sampled digital signals.
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A1.2.1 + A1.2.2 · Learn

Core knowledge and application

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A1.2.1Describe

The principal methods of representing data

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Exam moveGive a detailed, accurate account of what happens or what something is like.
Required detail 1Represent integers in binary and hexadecimal
Required detail 2Convert binary and hexadecimal integers to decimal, and vice versa
Required detail 3Convert integers from binary to hexadecimal, and vice versa

Explain it without notes

Describe: The principal methods of representing data in the context of a digital access-control circuit and data-encoding task.

  • Represent integers in binary and hexadecimal
  • Convert binary and hexadecimal integers to decimal, and vice versa
  • Convert integers from binary to hexadecimal, and vice versa
A1.2.2Explain

How binary is used to store data

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Exam moveGive the mechanism or relationship and make the reasons/causes explicit.
Required detail 1The fundamentals of binary encoding and the impact on data storage and retrieval
Required detail 2How data such as integers, strings, characters, images, audio and video are stored in binary form

Explain it without notes

Explain: How binary is used to store data in the context of a digital access-control circuit and data-encoding task.

  • The fundamentals of binary encoding and the impact on data storage and retrieval
  • How data such as integers, strings, characters, images, audio and video are stored in binary form
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Worked example · A1.2.1 / A1.2.2

Binary, hexadecimal and stored data

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Hex → binary → decimal

AC₁₆ = 1010 1100₂ = 172₁₀

Each hexadecimal digit maps to four binary bits: A = 1010, C = 1100.

Decimal → binary → hex

45₁₀ = 0010 1101₂ = 2D₁₆

Group binary into four-bit nibbles from the right to convert efficiently to hexadecimal.

Binary storage is a representation

Integers use bit patterns interpreted numerically; characters/strings use character encodings; images store pixel/sample information; audio stores sampled amplitudes; video combines sequences of encoded images with audio and metadata. The same physical 0/1 states can represent different kinds of data depending on the agreed encoding.

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Apply

Transfer to a new scenario

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ScenarioA digital access-control circuit and data-encoding task needs a design or technical decision related to today’s topic. Explain what matters and why.
  • Represent integers in binary and hexadecimal
  • Convert binary and hexadecimal integers to decimal, and vice versa
  • The fundamentals of binary encoding and the impact on data storage and retrieval
  • How data such as integers, strings, characters, images, audio and video are stored in binary form
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Exam lens

Paper 1 practice

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Build the response before checking notesUse precise terminology and match the required depth.
  1. Describe: The principal methods of representing data in the context of a digital access-control circuit and data-encoding task.
  2. Explain: How binary is used to store data in the context of a digital access-control circuit and data-encoding task.
Self-checkAnswer the exact command term. For explain, include mechanism/reason; for compare, pair criteria; for discuss/evaluate/justify, build supported reasoning and a conclusion.
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Homework

Finish the learning cycle

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IA — main task

Continue Criterion D development. Keep code readable, record meaningful implementation decisions, and maintain testing/evidence notes as you work.

Syllabus — short

Complete one targeted Paper 2/Paper 1 retrieval task from today’s lesson.

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End of Lesson 31.