What does base 2 mean?

Base 2 means numbers are built from groups of two instead of groups of ten. In base 10, ten ones make a ten, and ten tens make a hundred. In base 2, two ones make a two, two twos make a four, and two fours make an eight. That is why 100₂ stands for four, not one hundred.

How do you convert a number to binary?

One reliable way is to divide by 2 again and again, writing down each remainder. For 26: 26 divided by 2 is 13, remainder 0. Then 13 divided by 2 is 6, remainder 1. Next, 6 gives 3, remainder 0, and 3 gives 1, remainder 1. Finally, 1 gives 0, remainder 1. Read the remainders from last to first: 11010.

Is there a trick to check a binary answer?

Two quick checks catch most slips. A binary number ending in 1 is odd, and one ending in 0 is even, so 25 must end in 1. Also, a 0 added on the end doubles a binary number. An everyday number grows ten times that way, but 110₂ is 6 and 1100₂ is 12.

Why does my child read binary as normal numbers?

Binary uses the same digits as everyday numbers, so the eye reads 110 as one hundred and ten out of habit. Saying the digits one at a time, “one, one, zero”, breaks that habit and leaves room to work out the real value, six. The small 2 written after the digits is the signal to switch.

Is this binary numbers game free, and can a class play it?

Yes, a class can play both binary levels free, and pupils need only a web browser, with no sign-up and nothing to install. To warm up, write 1, 10 and 11 on the board as the start of a binary count. Pupils take turns adding the next number until someone writes 10000, which is sixteen. Then everyone fights on a tablet. For base conversion practice with progress tracking, the schools plan, priced per student, adds a teacher dashboard.

Math practice · reimagined

Number Bases Game

In this number base game you turn numbers from 2 to 31 into binary and back, so the longest binary number you meet is 11111. Your rival gets the same number, and whoever cracks it first sends their fighter swinging.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What are number bases?

A number base tells you how many digits a number system uses before it needs a new place. Everyday numbers are base 10: ten digits, 0 to 9, and after 9 comes 10. Binary is base 2, with just 0 and 1, so after 1 comes 10, meaning two. Binary counting goes 1, 10, 11, 100.

Every level of Binary

Example: what is 10011₂ as an everyday number?

The small 2 after 10011 tells you the number is written in base 2, binary.
Reading from the right, its five places are worth 1, 2, 4, 8 and 16.
The 1s stand in the 16, 2 and 1 places, so add 16 + 2 + 1 to get 19.
So 10011₂ is nineteen, and 19 is what you type on the keypad.

Learn it step by step

Computers count with only two digits, 0 and 1 — that's binary, or base 2. Each place is worth double the place to its right: 1, 2, 4, 8, 16…

To read a binary number, add up the place values wherever there's a 1. For 1011₂: the places (from the right) are worth 1, 2, 4, 8. There are 1s in the 1, 2, and 8 spots, so 8 + 2 + 1 = 11.

Add the values under each 1, and type the everyday number.

Tips and common mistakes

A row of 1s is always one less than the next place value. 111₂ is 7, one less than 8, and 11111₂ is 31, one less than 32.
A common mistake when writing binary is dropping the 0s. 18 is 16 + 2, so it is 10010: the empty 8, 4 and 1 places each still need a 0.
Let one hand stand for 16, 8, 4, 2 and 1: a raised finger means 1, a folded one 0. Ask your child to show 13, then 22.

How to play

One level shows a binary number such as 11101₂, and you type its everyday value, 29. The other asks for something like “20 in binary”, and you key in 10100, pressing only 0 and 1. Be first with the right digits and Broccoli attacks; the quicker you were, the more damage it does.

— Quick answers —

Binary: the short FAQ

What does base 2 mean?: Base 2 means numbers are built from groups of two instead of groups of ten. In base 10, ten ones make a ten, and ten tens make a hundred. In base 2, two ones make a two, two twos make a four, and two fours make an eight. That is why 100₂ stands for four, not one hundred.
How do you convert a number to binary?: One reliable way is to divide by 2 again and again, writing down each remainder. For 26: 26 divided by 2 is 13, remainder 0. Then 13 divided by 2 is 6, remainder 1. Next, 6 gives 3, remainder 0, and 3 gives 1, remainder 1. Finally, 1 gives 0, remainder 1. Read the remainders from last to first: 11010.
Is there a trick to check a binary answer?: Two quick checks catch most slips. A binary number ending in 1 is odd, and one ending in 0 is even, so 25 must end in 1. Also, a 0 added on the end doubles a binary number. An everyday number grows ten times that way, but 110₂ is 6 and 1100₂ is 12.
Why does my child read binary as normal numbers?: Binary uses the same digits as everyday numbers, so the eye reads 110 as one hundred and ten out of habit. Saying the digits one at a time, “one, one, zero”, breaks that habit and leaves room to work out the real value, six. The small 2 written after the digits is the signal to switch.
Is this binary numbers game free, and can a class play it?: Yes, a class can play both binary levels free, and pupils need only a web browser, with no sign-up and nothing to install. To warm up, write 1, 10 and 11 on the board as the start of a binary count. Pupils take turns adding the next number until someone writes 10000, which is sixteen. Then everyone fights on a tablet. For base conversion practice with progress tracking, the schools plan, priced per student, adds a teacher dashboard.

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