How to teach binary numbers to kids using a cool math trick?

A fun way to teach decimal to binary conversion to kids

Rajasekar Elango
Jul 31, 2019 · 5 min read

I got an opportunity to teach about computers to 6th-grade kids at Vidyarpana Montessori school in Coimbatore, India. In this article, I will share how I used a cool math trick to teach decimal to binary conversion and vice versa.

I started off with a question “Are computers smart? ” and talked through the first few slides of the presentation I gave earlier to Community Montessori School, Tampa.

You can read more about my computer science workshop at Community Montessori school in this post.

I explained to them the components of a computer and why computers know only the numbers “0” and “1”.

Let's play the game 🎮

To teach binary, I showed a cool math trick to read the number on anyone’s mind. To play the game, I made a poster with numbers 1 to 30 split into 5 columns like in the below table.

Then, Asked a student to

Think of a number

Then, look at the table and tell me only the columns in which the number she thought is present.

For e.g If a student told that the number is present only in column “C” and “E”, I immediately answered the number on her mind was “5”.

If you want to play this game interactively, check my blog.

We played this couple of the times and kids are amazed 😮

So, What’s the trick 😎 ?

When playing the game with one of the students, I made a wrong guess because of “incorrect” information, but that helped one of the other student to figure out the trick. The conversation went like this.

Student: My number is found in column “D” and “E”.

I: Your number is “3”.

Student: No.

I: Please look again and tell me exact columns you see your number.

Student: My number is also found in column “C”. So columns “C” , “D” and “E”.

I: Your number is “7”.

Another student, watching this conversation figured out the trick that we need to add numbers of the last columns. In this example
4 (C) + 2 (D) + 1 (E) = 7.

I am glad that this happened because students are able to learn from failure.

After revealing the trick, I asked if one any of them can come and perform this trick. A student volunteered and did it fantastically.

📘 How to create this magic table?

I asked if they want to learn to create the table by themselves and heard big enthusiastic Yes!

I used another poster with just table headers having numbers 16, 8, 4, 2, 1. Then I told them the logic to fill the table is

Based on this logic:

  • We wrote number “1” in the rightmost column just below “1”.
  • We wrote number “2” in the second rightmost column just under “2”.
  • We wrote number “3” in two rightmost columns “D” and “E” as 2 + 1 = 3.
  • We wrote number “4” in third rightmost columns under “4”.
  • We wrote number “5” in columns “C” and “E” as 4 + 1 = 5.
  • We wrote number “6” in columns “C” and “D” as 4 + 2 = 6.

With student’s help, we filled this table for a few more numbers.

🔢 Base 10 or Decimal System

The students are already familiar with Base 10 or Decimal system. I did a quick recap by expanding a decimal number e.g 541 in bases of 10.

Every one nodded that they already know how to write a decimal number in base 10 like this.

💻 What this trick has to do with binary numbers?

Above each column header, I wrote the number 0 or 1. Then, I told that

Each column value is represented as “0” or “1” depending on if a number is present or absent on the column.

For e.g since “6” is written on only column “C” and “D” , “6” can be written as 1 1 0

Then, we did an exercise to write each number in binary form.

We wrote

  • 1 1 0 for “6”
  • 1 1 1 for “7”
  • 1 0 0 0 for “8”
  • 1 0 0 1 for “9” etc.

How does this work ❓

Pay attention to numbers on the last row of the table.

This table is basically used write numbers in binary or base 2. i.e Each place represents a value that is the power of 2 like for decimal number, each place value represents the power of 10.

This is the reason we choose column header values like 16, 8, 4, 2, 1.

Then, I gave students some decimal number below 30 (for e.g 15) and asked them to fill the table in their notebook and answer back in binary. They were able to do it easily.

📒 Converting binary numbers to decimal.

We can easily convert binary numbers to decimal numbers similar to how we expand a number in base 10.

So, the decimal value for binary 1 0 1 0 is “10”.

I also give them some numbers in binary and asked them decimal value and they calculated it successfully.

📌 Why did we learn this?

We learned how to convert decimal numbers to binary and reverse binary back to decimal. Because the computer knows only binary and whatever information you enter will be converted to a binary like this and processed by computer.

If you like this post, please “clap” and share with others so that you can help reach more people.

Rajasekar Elango

Written by

I’m Rajasekar Elango, Principle Software Engineer at Salesforce.com. https://doculet.net/

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