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Magic calculator

By David Shaw, 27 March 2016

Cut out the six rectangles.

You will need

• A printout of the magic calculator sheet
• Scissors
• Someone to do the trick with

What to do

1. Cut out the six rectangles on the magic calculator sheet.
2. Ask your partner to think of a number between 1 and 63.
   

   Ask them to find all the cards with their number.

3. Hand the six rectangles to your partner. Ask them to look for their number and separate the cards that have their number on from the ones that don’t.
4. When your partner is finished, pick up all the cards that have their number on them.
5. Take the first number on each of those cards and add them together. This sum will be their number!

Add up the first number on each of the cards you received.

What’s happening?

This trick might look like magic. But it’s actually a maths trick! It’s also an introduction to the way that computers count.

There’s more than one way to write numbers. The normal way that we use is called decimal. Computers use a different way of writing numbers, called binary. Binary only has two digits: 1 and 0. In a computer, these two digits can correspond to ‘on’ and ‘off’ for electrical switches.

Binary numbers can do everything that regular, decimal numbers can do, but there are some differences. Since there are only two digits in binary, numbers have to be a lot longer. For example, 78 in decimal is written as 1001110 in binary.

Reading binary

Decimal is based around the number ten. As a result, we have a ones column, a tens column, a hundreds column and so on. Each column is ten times the value of the previous column.

Binary is based around the number two. It has a ones column, a twos column, a fours column, an eights column and so on. Each column is double the value of the previous column.

For example, the number 1001 has a 1 in the ones column and a 1 in the eights column. Its value is therefore one plus eight, or nine.

Each of the cards in this trick is focused on one digit of a number’s binary expression. If someone hands you the one and eight cards, then you know their number in binary has 1s in the ones and eights column, and 0s everywhere else. To work out the value of their number, you just have to add them up!

More information

Binary to decimal converter
Binary for beginners

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