How to Count in Binary with Fingers

Finger binary is a fantastic way to count in Base 2. You can use this approach to count from 0 to 31 using the fingers on a single hand, or from 0 to 1023 if you’re using both your right and left. You probably haven heard of it before, but it’s a trending subject among math enthusiasts.

Our conventional base-ten system has digits for the numerals zero-nine. There’s no unit for “ten.” We may write “10,” but it’s actually “1” ten and “0” ones. After a digit reaches 9, the next increment resets it to 0 but causes an increase of the next digit on the immediate left.

The only reason decimal numbers feel natural and binary digits donâ€™t is that youâ€™ve counted in base 10 since you were a child. Also, nearly every culture has used base-ten mathematics. This is likely because we have 10 fingers. If we had four digits on each hand, like spider monkeys, our natural counting system would probably have been octal or hex (hexadecimal).

Like the decimal number system, binary counting relies on positional notation. The only difference being that it is base-2 instead of base 10. The decimal system works with powers of 10 and uses 10 unique symbols (0-9) as earlier mentioned. Binary numbers work with base-2. That means they rely on powers of 2 to express significance. They comprise only two unique symbols: 0 and 1.

Finger binary might seem hard, but itâ€™s an easy counting method to learn. it gets even easier if you’ve done Chisanbop (Korean finger counting) or watched the mathematician James Tanton on TED-Ed.

Letâ€™s work with something really simple as an example: counting to 31.

First, mark the fingers of your hand with the following numbers in a non-permanent, skin-friendly marker: 1, 2, 4, 8, 16. Remember to start with your rightmost digit (since we’ll be using our right hand for this demonstration). If you’d rather use your left hand, start with your left-most finger.

Close your fist. This represents 0 in the binary system.

With the rest of your fingers closed. Raise your right thumb. It should have the number 1 on it. It represents 1 in the binary system.

Note: each closed finger represents “0,” and an open finger represents 1.

Now close your thumb and raise your index finger, which should be marked with the number 2. This will be written as 10 in binary. The index finger represents 1, and your thumb, which is currently closed, means “0”.

Raising your thumb and index finger will give you 3, which you’ll write as 112.

Now close both your index and thumb and raise your middle finger. (You’re not doing anything obscene here; itâ€™s just to represent the number 4). Since each raised finger represents 1 and each closed finger to its right is represented as a “0,” you’ll write this as 100 in binary (1002).

Keep your middle finger up, then raise your thumb too.  “4” plus “1” gives you 5, which you’ll write as 1012.

Put your thumb back down and raise your index finger along with your middle finger. It should give you “4” and “2,” or a total of 6. You’ll write this as 110 in binary.

Now raise your thumb, index, and middle fingers.  Adding “4,” “2,” and “1” gives you 7, written as 111 in binary.

Next, make a fist, then raise your ring finger. It represents 8, which you’ll write as 10002.

To make 9, extend your thumb and ring finger. This is written as 10012.

Close your thumb and raise your index, leaving your ring finger extended. This makes 10, or 10102

Your thumb, index, and ring finger give you 11, written as 10112.

Raising your ring and middle finger should make 12. (11002) in binary

To make 13 (11012), extend your thumb, middle, and ring fingers.

Closing your thumb while opening your index, middle, and wedding fingers makes 14 or 11102

To get to 15 (11112), raise your thumb, index, middle, and ring fingers.

Now make a fist and extend your little finger. This makes 16 in base 10 or 10000 in binary.

Next, raise your pinky and thumb to get 17 (100012).

The combination of your index and pinky gives you 18 (100102)

Your thumb, index, and pinky will give you 19 (10011).

Extend your middle finger and pinky to make 20 (101002)

Your pinky, middle finger, and thumb make 21 (101002).

Your index, middle, and pinky make 22 (101102).

Raise your pinky and ring finger to make 24 (110002).

Put your thumb and middle finger down. This will leave your pinky, ring finger, and index raised, making 26 (110112).

To make 27 (110112), raise your thumb, pinky, ring finger, and index finger.

For 28 (11100), you’ll want to raise your pinky, ring finger, and middle finger.

Next, keep your pinky, ring finger, and middle finger raised, then add your thumb. This makes 29 or (111012).

Raising all four fingers beside your thumb gives you 30 (11110).

Extending all 5 fingers gives you 31

This article has covered the basics of finger counting in binary. Sure, it looks complicated. But, if you’ve read this far, you’ve likely realized it’s not that hard.

Remember: If you’re doubting the validity of your counts, you can use our binary to decimal converter to check your accuracy.