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MMathematicsICTS2 to S4Number

Binary lab: number bases, indices and standard form

Every photo, song and message on a phone is stored as 0s and 1s. Switch the bits yourself and find out how big a photo really is.

💡101101₂ = 45binary, number bases and indices
LevelS2 to S4 (and IGCSE)
TimeAbout 35 min
You usePlace value, indices
PriceFree: no account

🎯 Aim

To convert between number bases and use indices and standard form with digital data.

You will learn to

  • Convert between base 10, base 2 and other bases.
  • Explain place value in any base.
  • Use the laws of indices.
  • Write large and small numbers in standard form.

🧭 What to do

  1. Tap the bulbs to make a binary number and read its value.
  2. Use the slider and read the number in other bases.
  3. Change the Megapixels and read the photo size in standard form.
  4. Look at how many values n bits can store.
  5. Answer the questions with the class data.
  6. Write your conclusion and download your lab report.

🔬 Lab bench

📋 The data

Numbers 0 to 16 in four bases.

🧠 Investigate: answer from the data

Type your answer and tap Check. Use 💡 Hint first; open the method only when you are stuck.

📄 My lab report

Your report collects the aim, your data table, the graphs, your answers and your conclusion. It is made on your phone or computer: nothing is sent to anyone.

Check your conclusion

In base 2 each place is a power of 2 (1, 2, 4, 8, …), so 101101₂ = 32 + 8 + 4 + 1 = 45. A byte of 8 bits stores 2⁸ = 256 values (0 to 255 = FF₁₆). Indices laws (2ᵃ × 2ᵇ = 2ᵃ⁺ᵇ) and standard form make it easy to work with very large data sizes.

➕ Get more from this experiment

📝 Free

Print the worksheet (button above), download the data, and save your report. Teachers can project this page in class.

📦 Premium Lab Pack

1 000 RWF

  • Worksheet: binary cards and secret messages
  • Number bases and indices problems
  • Teacher guide and answer key
  • Exam-style questions with marking scheme

👩‍🏫 For teachers

Use it as a practical when apparatus is missing, as homework, or as a project. Free lesson plans help you plan, teach and assess.

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