Binary and addition
Printable Binary Cards: Download, Cut Out and Start Flipping
Download the card PDF in your language and print it single-sided on A4 at actual size. Cut out the five cards worth 16, 8, 4, 2 and 1 from page one, then follow the steps on page two to build five target numbers and check your answers.
What's in the PDF
The PDF has two portrait A4 pages and reads clearly in black and white. Page one has five point cards worth 16, 8, 4, 2 and 1; cut along the borders. The cards are printed on one side only, with blank backs.
Page two has the steps, five target numbers and their answers. Print at 100% or actual size, and have an adult help with the cutting.
How to flip the cards
The printed side up means 1, and the blank back up means 0. Lay the cards out left to right as 16, 8, 4, 2, 1.
- Before you start, turn all five cards face down and set the amount still needed to the target.
- Look at the cards from 16 down to 1.
- If the amount still needed is greater than or equal to the card's points, turn it up and subtract its points.
- Otherwise leave it face down, keep the amount the same, and move to the next card.
- After five cards the amount still needed should be 0. Read the 1s and 0s from left to right.
Five targets and answers
Try each one before checking this table. Leading zeros don't change the value, so 01001₂ is just 9.
| Target | Binary | Face-up cards |
|---|---|---|
| 0 | 00000₂ | None, all face down |
| 9 | 01001₂ | 8, 1 |
| 18 | 10010₂ | 16, 2 |
| 23 | 10111₂ | 16, 4, 2, 1 |
| 31 | 11111₂ | 16, 8, 4, 2, 1 |
Why there is no 32 card
Five cards reach at most 11111₂, which is 16+8+4+2+1=31. All face down is 00000₂, which is 0.
To show 32 you would need a sixth card worth 32 on the far left. This PDF has only five cards, so every target is between 0 and 31.
Check yourself
What does a row of five face-down cards mean?
Answer
It means 0, written 00000₂. Every card is 0 and no points are added, but 0 is still a number.
Which cards do you turn up to make 18?
Answer
Start at 16: 18 is at least 16, so turn it up and 2 is still needed. 8 and 4 are more than 2, so leave them down. 2 equals 2, so turn it up and 0 is needed. Leave 1 down. That is 16 and 2, written 10010₂.
Can these five cards show 32?
Answer
No. With all five face up the most is 31. 32 needs a sixth card worth 32, written 100000₂.