Binary and addition
Binary Numbers for Kids, Explained Simply with Cards
Binary counts with only two digits, 0 and 1. Lay out a row of cards. A face-up card means 1 and a face-down card means 0. Add the points on the face-up cards and you get the value of the binary number.
Face up is 1, face down is 0
Start with what you can see: a row of cards, each one either face up showing its points or face down. We write face up as 1 and face down as 0.
The whole row then becomes a string of 0s and 1s. That string is a binary number, and each card is one digit, or bit.
Each card's points are its place value
From left to right the five cards are worth 16, 8, 4, 2 and 1. Each card to the left is worth twice as much. Where a card sits decides what it is worth when face up. That is place value.
To show 9, turn up only the 8 card and the 1 card, because 8 plus 1 is 9. Reading left to right gives 01001₂. The leading 0 means the 16 card is face down, and writing it does not change the value.
01001₂ = 8 + 1 = 9
Five cards show 0 to 31
With all five cards face down you have 00000₂, which is 0. Zero is a real number, not a missing one.
With all five face up you have 11111₂, which is 16+8+4+2+1, or 31. That is the largest number five cards can show.
To show 31 plus 1, which is 32, five cards are not enough. You need a sixth card worth 32 on the far left, written 100000₂.
| Binary | Face-up cards | Decimal |
|---|---|---|
| 00000₂ | None | 0 |
| 00001₂ | 1 | 1 |
| 01001₂ | 8, 1 | 9 |
| 11111₂ | 16, 8, 4, 2, 1 | 31 |
Reading binary as a decimal number
To read a binary number, give the digits place values of 1, 2, 4, 8 and 16 starting from the right, then add the place values of the digits that are 1.
For 10110₂: the 16 place is 1, the 8 place is 0, the 4 place is 1, the 2 place is 1 and the 1 place is 0. That makes 16+4+2, which is 22.
Check yourself
Which cards do you turn up to show 6 with five cards? How is it written in binary?
Answer
Turn up the 4 card and the 2 card, because 4 plus 2 is 6. With five digits it is 00110₂.
What does a row of five face-down cards mean?
Answer
It means 0, written 00000₂. Zero is still a number; no points are being added.
What is the largest number five cards can show, and what do you need for 32?
Answer
The largest is 11111₂, which is 31. For 32 you need a sixth card worth 32, written 100000₂.