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number bases

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: number bases

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about number bases. Then check against the key terms: A number base (or radix), Decimal, Why do humans use base 10?. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: A number base (or radix), Decimal, Why do humans use base 10?.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: number bases. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Computer Science because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: What is the decimal value of binary 10110?

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about number bases.

Lesson 2: Core Concepts: number bases

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on number bases. Check them against the notes below.

Main Content (35 minutes)

A number base (or radix): is the number of unique digits used to represent numbers in a positional numeral system. The position of each digit determines its value - this is called positional notation.
Decimal: is the number system we use every day. It has 10 digits (0-9). Each position represents a power of 10: units, tens, hundreds, thousands, etc.
Why do humans use base 10?: Most likely because we have 10 fingers! There is nothing mathematically special about base 10 - it is just what we are used to.
Binary: uses only two digits: 0 and 1. Each position represents a power of 2. Binary is the fundamental language of computers because electronic circuits have two states: on (1) and off (0).
Computers use binary: because their hardware is built from billions of transistors, which are electronic switches with exactly two states: ON (electricity flowing) and OFF (no electricity flowing). These two states map perfectly to 1 and 0.
Key point: If we tried to use more states (e.g. base 10 with 10 voltage levels), it would be much harder to distinguish between similar values, especially with electrical interference. Binary's two clear states make it incredibly reliable.
TermMeaningExample
Base 10Decimal / Denary0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base 2Binary0, 1
Base 16Hexadecimal0-9, A, B, C, D, E, F
000000000
000000011
0000101010
01100100100
11111111255

Practice (10 minutes)

Q: What is the decimal value of binary 10110?

Answer: 1x16 + 0x8 + 1x4 + 1x2 + 0x1 = 16 + 4 + 2 = 22

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: number bases

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: A number base (or radix), Decimal, Why do humans use base 10?. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Q1: What is the decimal value of binary 10110?

Answer: 1x16 + 0x8 + 1x4 + 1x2 + 0x1 = 16 + 4 + 2 = 22

Q2: What is the decimal value of hex 2F?

Answer: 2 x 16 + 15 x 1 = 32 + 15 = 47

Q3: Why do computers use binary instead of decimal?

Answer: Computers use binary because their hardware consists of transistors that have only two states: on (1) and off (0). This makes binary the natural representation for electronic circuits. Using only two states also makes it reliable and easy to distinguish between values even with electrical noise.

Q4: Why is hexadecimal used instead of binary when humans read computer data?

Answer: Hexadecimal is used because one hex digit represents exactly 4 binary bits, making it a compact and easy-to-read shorthand for binary. A 16-digit binary number like 1111111111111111 becomes just FFFF in hex. It is much easier for humans to read and less error-prone than long binary strings.

Q5: What decimal number does the hex digit C represent?

Answer: C = 12 in decimal.

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: number bases

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Full-Mark Response Convert the decimal number 156 to binary and to hexadecimal. Show your working for each conversion. [4 marks] <div class="

Decimal to Binary (divide by 2, record remainders): 156 ÷ 2 = 78 r 0 78 ÷ 2 = 39 r 0 39 ÷ 2 = 19 r 1 19 ÷ 2 = 9 r 1 9 ÷ 2 = 4 r 1 4 ÷ 2 = 2 r 0 2 ÷ 2 = 1 r 0 1 ÷ 2 = 0 r 1 Read remainders bottom-up: 10011100 Decimal to Hexadecimal (divide by 16): 156 ÷ 16 = 9 remainder 12 9 ÷ 16 = 0 remainder 9 12 = C in hex Read remainders bottom-up: 9C So 156₁₀ = 10011100₂ = 9C₁₆

Exam Tips: Remember: computers ONLY use binary internally - hex is for human convenience | Binary place values double each position: 1, 2, 4, 8, 16, 32, 64, 128 | Hex place values multiply by 16: 1, 16, 256, 4096 | Each hex digit = exactly 4 binary bits | Know the hex digits: A=10, B=11, C=12, D=13, E=14, F=15 | When explaining why binary: mention transistors, on/off states, reliability
Common Errors: ✗ Thinking binary digits can be 0, 1, or 2 ✓ Binary (base 2) only uses digits 0 and 1. The digit 2 is invalid in binary — 2 in decimal is 10 in binary. ✗ Confusing the place values of different number bases ✓ Binary place values are powers of 2 (1, 2, 4, 8, 16...), hexadecimal uses powers of 16 (1, 16, 256...), and decimal uses powers of 10 (1, 10, 100...). ✗ Thinking hexadecimal is a different number system from binary in terms of storage ✓ Hexadecimal is a shorthand representation of binary for human readability. Each hex digit represents 4 binary bits; the computer still stores binary. ✗ Believing that 10 in binary equals 10 in decimal ✓ 10 in binary equals 2 in decimal. 10 in hexadecimal
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how number bases connects to another Computer Science topic you have studied
  • Real-world: research one real-world use or example of number bases
  • Critical: "What are the limitations of the models used in number bases?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

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