Pi in binary

General Memory Chat
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Hello, I’m trying to memorize some digits of pi in binary, but cant seen to find an accurate way to consistently get the correct numbers. Are there any official websites or anything to give me the legitimate binary for it?
Thanks

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Never thought about doing this before. Wouldn’t it depend on how many digits you encode per binary sequence? And if you drop the leading zeroes?

I know your question isn’t about the memorizing process itself, but I’m interested in thinking through what that would look like if someone asked me to do it…

At minimum, you’d need 4 binary digits to represent the decimal digits 0-9. Optionally, you can drop the leading zeroes without losing information.

0 = 0000 (or 0)
1 = 0001 (or 1)
2 = 0010 (or 10)
3 = 0011 (or 11)
4 = 0100 (or 100)
5 = 0101 (or 101)
6 = 0110 (or 110)
7 = 0111 (or 111)
8 = 1000
9 = 1001

so 3.141592 converted to 4-digit binary sequences per decimal digit would be:
0011. 0001 0100 0001 0101 1001 0010…

If you drop the leading zeroes then it becomes:
11. 1 100 1 101 1001 10

But I’d think that makes it much tougher to convert to imagery to store and recall. If you have a 3-digit number system you could do it, with the addition of two special indicators for 1000 and 1001.

You have to just take each digit and keep converting as you go. Is this similar to how you plan to memorize this?

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I don’t think it’s a matter of converting the decimal digits one by one like that. That gives you a binary number, but it’s not pi in binary.

The binary representation of pi starts like this:

11.00100100001111110110…

which is 2 + 1 + 0/2 + 0/4 + 1/8 + 0/16 + 0/32 + 1/64 + …

but I don’t know how to calculate lots of digits without reaching the limit of the calculator or spreadsheet.

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4

Ohhhhhh! I think I see?

So its basically converting something like 1415926535/10000000000ths into the equivilent binary “fraction” (right side of the decimal)?

According to one calculator website I found:
3.1 is 11.0001100110011001101
3.14 is 11.00100011110101110001
3.141 is 11.00100100000110001001

Oof. This isn’t as simple as just adding additional binary digits to represent additional decimal digits. It changes the entire binary sequence when you extend the number of decimal digits.

So then I suppose you need to decide how many decimal digits you want to go for ahead of time because its not as simple as just going “ok, I’m gonna learn 3.141592 today and tomorrow I’ll add 10 digits and get to 3.1415926535897932.” If you decide to memorize a longer binary representation, you have to start over at 3 (or “11”) because the rest of the sequence will be totally different?

Either way… Fascinating. But, ow my brain.

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5

maybe you can group numbers into certain length and convert that to binary

6

Another way of thinking of it is:

  • is pi > 3 1/2? No, so the first binary digit is 0 [11.0 representing 3 0/2 or 3 0/4]
  • is pi > 3 1/4? No, so the next binary digit is 0 [11.00 representing 3 0/4 or 3 0/8]
  • is pi > 3 1/8? Yes, so the next binary digit is 1 [11.001 representing 3 1/8 or 3 2/16]
  • is pi > 3 3/16? No [11.0010 representing 3 2/16 or 3 4/32]
  • is pi > 3 5/32? No [11.00100 representing 3 4/32 or 3 8/64]
  • is pi > 3 9/64? Yes [11.001001 representing 3 9/64] etc.
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7

That’s helpful, thanks!

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The site has 1 million binary digits of pi: One Million Binary Digits of Pi
But the file on the site is in binary format. So I converted it to txt using python.
pi.txt (1,0 МБ)

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