Binary and addition

Binary Cards Activity: A Binary Counting Game

All you need is five cards with points written on them. For each target number, turn up the cards whose points add up to exactly that number, then write face up as 1 and face down as 0.

Make the cards

Take five slips of paper and write 16, 8, 4, 2 and 1 on the fronts, leaving the backs blank. Lay them out left to right as 16, 8, 4, 2, 1, all face down.

You can also open the free card lesson on the website and use the cards on screen. The game works the same way.

How to play

For each round, read the target, try it with your own hands, and only then check the answer table.

At the start of each round, turn all five cards face down and set the amount still needed to the target.
Look at the cards one at a time, starting with the 16 card on the left.
If the card's points are no more than the amount still needed, turn it up and subtract its points from that amount.
If the card's points are more than the amount still needed, leave it face down, keep the amount the same, and move to the next card.
After all five cards, the amount still needed should be exactly 0, and the face-up points add up to the target.
Write face up as 1 and face down as 0 from left to right to get the binary form.

Place value

160

01001₂ = 8 + 1 = 9

Worked example for 9: of the cards 16, 8, 4, 2 and 1 from left to right, only 8 and 1 are face up, written 01001₂. Try the other targets yourself before checking the table.

Five targets and answers

Work through 3, 9, 18, 23 and 31 in order. Finish each one before you look at its row below.

Target numbers and face-up cards
Target	Face-up cards	Binary
3	2, 1	00011₂
9	8, 1	01001₂
18	16, 2	10010₂
23	16, 4, 2, 1	10111₂
31	16, 8, 4, 2, 1	11111₂

Common mix-ups

More face-up cards does not always mean a bigger number. The 16 card alone beats 8, 4, 2 and 1 together, which make 15. Position matters more than how many.

All cards face down is not "no number". It is 00000₂, which is 0.

Do not read binary as decimal. 01001₂ is not one thousand and one; it is 9.

Five cards cannot make every number. They stop at 31, and 32 needs a sixth card worth 32.

Check yourself

Which cards do you turn up to make 12?
Answer
Turn up 8 and 4, because 8 plus 4 is 12, written 01100₂.
Why is the single 16 card worth more than 8, 4, 2 and 1 together?
Answer
8+4+2+1 is 15, and 16 is more than 15. Each card is worth one more than all the cards to its right added together.
What number is 10010₂?
Answer
The 16 and 2 places are 1, and 16 plus 2 is 18.