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Binary Cards

Computing · Year 4–Year 6

Turn the cards over to make a number, and read it in 1s and 0s.

About the binary cards

Five cards with dots on: 16, 8, 4, 2 and 1. Turn a card face up and its dots count, turn it face down and they do not, and the number under the cards changes as you go.

EVERY NUMBER FROM 0 TO 31 CAN BE MADE, and each one only one way. That is the whole of what binary is, and a class finds it out by trying to make the same number twice and failing.

Each card is the one to its right with its dots doubled: one, then two side by side, then two by two, then four by two, then four by four. The doubling is drawn rather than stated, and it is why five cards reach as far as thirty-one.

Add 1 is the question worth asking. What happens to the cards when you add one to seven? Three of them turn face down and a fourth turns face up, all at once, which is carrying in a base a class has never carried in before.

The row of digits under the cards is the number in binary, in the same order as the cards, so a class can read 10110 straight off the board.

How to use it on your whiteboard

  1. 1Tap a card to turn it over.
  2. 2Ask the class to make a number: their age, the date, the number of children in the room.
  3. 3Ask whether it can be made a different way, then try.
  4. 4Press Add 1 and watch which cards turn over.
  5. 5Read the 1s and 0s under the cards out loud.
  6. 6Tap All down to start again, or Undo to take back the last card.

Questions

Why these five numbers?
Because each is double the one before it, so between them they make every number up to thirty-one and each number only one way. Add a 32 card and you reach sixty-three, and so on.
What is the biggest number five cards can make?
Thirty-one, with every card face up: 16 + 8 + 4 + 2 + 1. That is one less than thirty-two, which is the next card, and it is not a coincidence.
How does this connect to how computers store things?
A card is a bit: it is on or it is off, and there is nothing in between. Pixel Pictures is the same idea drawn as a picture, where each square of the grid is one bit.