Counting in Binary with Dot Cards

No adult supervision needed: paper and a pen only.

Protective equipment and “do not substitute” warnings have not been recorded for this experiment yet. They are added when its safety review is completed; until then, follow the supervision notes above.

Disposal: Recycle the paper, or keep the cards for next time.

Materials

• Five index cards or sticky notes
• A pen

Steps

1. Draw dots on the cards: 1 dot on the first, 2 on the next, then 4, then 8, then 16.
2. Lay the cards face up in a row with 16 on the left and 1 on the right.
3. A card that is face up counts as 1 and adds its dots; a card that is face down counts as 0.
4. Turn cards over to make the number 5 (only the 4 card and the 1 card face up). Write it as 00101.
5. Make every number from 0 upwards, writing each pattern of 1s and 0s. Try the biggest number you can make.

What you should see

• Each card has twice as many dots as the card to its right.
• Every number from 0 to 31 can be made, each in exactly one way.
• With all five cards face up the total is 31 (11111); making 32 would need a sixth card with 32 dots.

Why it works

Computers store numbers and all other information using binary digits, or bits, each of which is either 0 or 1. Each card is one bit: face up for 1, face down for 0.

Because each card is worth double the one before it, five cards can represent every whole number from 0 to 31: 32 different values. Each extra bit doubles the number of values you can store.

Learn the ideas behind it

• Computers
• Memory

Sources

• How binary digits work — CS Unplugged (University of Canterbury)