converting number bases
4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.
Lesson Overview
Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Learning Objectives
- Explain the key ideas of converting number bases
- Apply converting number bases to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for converting number bases first (GCSE Revise summary)
- Key vocab to pre-teach: Method, Method, Method
- Basic skills: reading the summary notes and answering the practice questions there
Materials & Equipment
- Exercise book, coloured pens
- Ruler
- Printed revision notes (link below)
- Internet for videos (see Resources)
Lesson 1: Introduction: converting number bases
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about converting number bases. Then check against the key terms: Method, Method, Method. Use a mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Method, Method, Method.
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.
Before lesson: Read the script below. Pre-teach key vocab: Method, Method, Method.
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: converting 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.
Mins 0-5 - Hook: "Today: converting 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: Convert binary 11001010 to decimal.
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about converting number bases.
Lesson 2: Core Concepts: converting number bases
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on converting number bases. Check them against the notes below.
Main Content (35 minutes)
You need to be able to convert between all three number bases: decimal (base 10), binary (base 2), and hexadecimal (base 16). There are six possible conversions to master.
Method: Write out the binary place values above each bit. Add up all the place values where there is a 1. Ignore positions with a 0.
Method: Repeatedly divide the decimal number by 2. Record the remainder each time (it will always be 0 or 1). Read the remainders from bottom to top to get the binary number.
Method: Find the largest power of 2 that fits into the number. Subtract it and put a 1 in that position. Repeat with the remainder. Put 0s in positions where the power doesn't fit.
Method: Multiply each hex digit by its place value (powers of 16) and add the results together. Remember: A=10, B=11, C=12, D=13, E=14, F=15.
Method: Repeatedly divide the decimal number by 16. Record the remainder each time. Convert remainders 10-15 to A-F. Read the remainders from bottom to top.
| Term | Meaning | Example |
|---|---|---|
| Binary | Decimal | Add up positional values where bit is 1 |
| Decimal | Binary | Repeated division by 2 (or subtract largest power of 2) |
| Hex | Decimal | Multiply each digit by its place value and add |
| Decimal | Hex | Repeated division by 16 |
| Binary | Hex | Group bits into fours, convert each group |
| Hex | Binary | Expand each hex digit to 4 bits |
| Reading division remainders top-to-bottom | The first remainder is the least significant bit | Always read remainders from BOTTOM to TOP |
| Not padding binary groups to 4 bits | Hex 3 = 0011, not 11 | Always use 4 bits per hex digit, pad with leading zeros |
Practice (10 minutes)
Q: Convert binary 11001010 to decimal.
Answer: 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 = 202
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: converting number bases
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: Method, Method, Method. 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: Convert binary 11001010 to decimal.
Answer: 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 = 202
Q2: Convert decimal 200 to binary (8 bits).
Answer: 200 - 128 = 72, 72 - 64 = 8, 8 - 8 = 0. Binary: 11001000
Q3: Convert hex A5 to decimal.
Answer: A x 16 + 5 x 1 = 10 x 16 + 5 = 160 + 5 = 165
Q4: Convert binary 111100001010 to hex.
Answer: Group: 1111 0000 1010 = F0A
Q5: Convert hex 2F to binary.
Answer: 2 = 0010, F = 1111. Binary: 00101111
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: converting 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 hexadecimal number 3F to binary and then to decimal. Show all working. [3 marks] <div class="
Hex to Binary: 3 = 0011 F = 1111 3F = 00111111 Binary to Decimal: 00111111 0×128 + 0×64 + 1×32 + 1×16 + 1×8 + 1×4 + 1×2 + 1×1 = 0 + 0 + 32 + 16 + 8 + 4 + 2 + 1 = 63 So 3F₁₆ = 00111111₂ = 63₁₀
Exam Tips: Write out the place values above each binary digit - it prevents mistakes | For binary-to-hex, group from the RIGHT in groups of 4 | For hex-to-binary, always write 4 bits per hex digit (pad with zeros) | Division remainders are read BOTTOM to TOP | Practise all six conversions until they become automatic | In the exam, show your working - you can get partial marks
Common Errors: ✗ Padding binary with zeros on the wrong side when converting to hex ✓ When grouping binary into 4-bit groups for hex conversion, pad with leading zeros on the LEFT, not trailing zeros on the right. ✗ Forgetting that hex digits A-F represent 10-15 ✓ A=10, B=11, C=12, D=13, E=14, F=15. These are single hex digits, not two-digit numbers. F is 15, not 16. ✗ Adding binary without carrying when the column sum exceeds 1 ✓ In binary addition: 0+0=0, 0+1=1, 1+1=10 (0 carry 1), 1+1+1=11 (1 carry 1). You must carry just like in decimal addition. ✗ Converting binary to hex by converting each bit individually instead of grouping in fours ✓ Group binary into sets of 4 bits from the right, then convert ea
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how converting number bases connects to another Computer Science topic you have studied
- Real-world: research one real-world use or example of converting number bases
- Critical: "What are the limitations of the models used in converting 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
- Consolidation: Re-answer any Lesson 3 practice questions answered incorrectly (20 mins)
- Retrieval: Write flashcards for the key terms: Method, Method, Method (10 mins)
- Exam practice: One past-paper question on converting number bases from the board websites (15 mins)
- Extension: Explain converting number bases to someone else in your own words (10 mins)