Learn binary

9 short steps, from one bit to your first grid. About 2 minutes.

Step 1 of 9

One bit

A bit is a switch: off is 0, on is 1. Switch it on to match the target on the right.

Two bits

The left bit is worth 2, twice the right one. Add up the bits that are on: two bits count from 0 to 3. Make each target.

Three bits

The next bit is worth 4, so three bits reach 7. Count from 4 to 7: the 4 stays on while the other two bits count again.

Four bits

8, 4, 2 and 1: four bits reach 15. Start with the biggest bit that fits into the number, then make the rest with the smaller ones.

A second row

Now there are two rows. The top one is done. Make 9 in the bottom one. The small number in the target is your sum. It turns orange when you go over.

6 6

9 0

Columns are numbers too

Read each column from top to bottom, like a row turned on its side. Its place values now run down the left side, and its target is underneath.

6 6

9 9

1 1

2 2

1 1

One bit, two numbers

Every bit sits in one row and one column. Switch any bit and watch both of its targets.

6 6

9 9

1 1

2 2

1 1

Find the wrong bit

One bit is wrong, so one row and one column miss their targets. The wrong bit is where they cross.

5 5

6 7

3 3

6 6

3 3

5 7

Your first grid

The top row is done. Finish the other two, and the columns check your work.

Binary numbers from 0 to 15

Decimal	Binary	Sum of place values
0	0000	0
1	0001	1
2	0010	2
3	0011	2 + 1
4	0100	4
5	0101	4 + 1
6	0110	4 + 2
7	0111	4 + 2 + 1
8	1000	8
9	1001	8 + 1
10	1010	8 + 2
11	1011	8 + 2 + 1
12	1100	8 + 4
13	1101	8 + 4 + 1
14	1110	8 + 4 + 2
15	1111	8 + 4 + 2 + 1

Decimal and binary

Decimal numbers use ten digits, and every place is worth ten times the one to its right. Binary uses only 0 and 1, and every place is worth twice the one to its right: 1, 2, 4, 8, 16 and so on.

To write 13 in binary, take the largest place value that fits: 8, which leaves 5. Next, 4 fits, which leaves 1. The 2 does not fit, so that bit is 0. The 1 fits. Read the bits from left to right: 1101.

To go back, add up the place values of every 1: 1101 is 8 + 4 + 1 = 13.

Tips for faster solving

Odd numbers always end in 1, even numbers in 0. Set the last bit first.
The first bit is on when the number is at least its place value: 8 or more with four bits.
Learn the powers of two by heart: 1, 2, 4, 8, 16, 32, 64, 128.

Questions

How do you convert a decimal number to binary?

Start with the largest place value that fits into the number and switch that bit on. Subtract it, then repeat with the remainder for the next smaller place values. Every place value you used is a 1, every one you skipped is a 0. For example, 13 = 8 + 4 + 1, so 13 in binary is 1101.

How do you convert binary to decimal?

Write the place values over the bits, from 1 on the right and doubling to the left. Add up the place values of every bit that is 1. For example, 1011 is 8 + 2 + 1 = 11.

What is the largest number n bits can show?

With n bits you can show numbers from 0 to 2ⁿ − 1. Four bits go up to 15, six bits to 63 and eight bits (one byte) to 255.

Why does the game have column targets as well?

The row targets alone decide the answer, because every number has exactly one binary form. The column targets read the same bits from top to bottom. One wrong bit breaks both its row and its column, so you find it where the two cross.

Can I use the Binary Game in class?

Yes. It is free, needs no account or installation and works on phones, tablets and projectors. Start with this page, then play with 4 bits and move up once the place values feel familiar.