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Binary to Decimal

Each of the 24 lines, consisting of 11 binary digits, must be converted to a decimal number manually on your airgapped computer or by using paper and pen. This is important because using online tools to convert binary to decimal could expose your seed phrase, which would compromise your security.

A bit about binary: In the binary system, there are only two digits: 0 and 1. The digits we’re familiar with (2, 3, 4, etc.) don’t exist here. So when counting, we start with 0, then 1. But after 1, there's no "2." The next number after 1 is “10” in binary, which is read as "one, zero" (not "ten"). This represents the decimal number 2. The next binary number is “11” ("one, one"), which is 3 in decimal.

In binary, the numbers increase like this:

  • “100” is 4,
  • “101” is 5,
  • “110” is 6,
  • “111” is 7,
  • “1000” is 8,
  • “1001” is 9, and so on.

With 11 binary digits, the smallest number is 0 (00000000000), and the largest is 2047 (11111111111).

To convert each line of binary digits, simply take each 11-digit sequence and convert it to decimal. You can do this in 2 ways:

Airgapped Computer​

For example, to convert the first line, whose number is 10111000101, you’d type:

echo $((2#10111000101))

This will output 1477. You just need to replace the binary digits in the command with each 11-digit binary number and run the calculation.

Paper & Pen​

At the top left of your page, write the following numbers from left to right, aligned with the binary digits below. Start with 1024 above the first column, then 512 above the second column, 256 above the third, and so on, halving the number each time until you reach 1 above the last (eleventh) column on the right.

Now, for each binary digit:

  • If the digit is 1, write down the decimal number directly above it.
  • If the digit is 0, write 0 or skip that number.

Add up all the numbers you wrote down. This sum is the decimal equivalent of the binary number.

For example, to convert the first line, whose number is 10111000101, you'd do:

1024+0+256+128+64+0+0+0+4+0+1

This will output 1477 which is the same number we got with the airgapped computer method.

Repeat this process for all 24 rows. You’ll now have 24 decimal numbers, each ranging from 0 to 2047.

#10245122561286432168421TOT
1)101110001011477
2)110111001001764
3)101111001111511
4)01101000101837
5)111110101012005
6)111110010001992
7)00100000101261
8)101110001011477
9)101010101001364
10)101110111011501
11)111110001011989
12)01111001110974
13)101110101001492
14)100110001111223
15)101110001111479
16)111110111012013
17)00011000101197
18)101010001101350
19)111110101002004
20)111110001001988
21)00101000101325
22)101110101011493
23)100110001011221
24)00101010010338