Binary translator that reads both directions

Paste the digits into the top box with the page set to Binary → text and the sentence appears underneath. Spacing is optional, because an unbroken run is cut into groups automatically whenever its length divides evenly by 8, 7 or 16. If what comes back is gibberish rather than English, the encoding menu is on the wrong setting — try UTF-8 first, then Latin-1, which is what most pre-2005 Western European text was written in.

Because a group of digits is only a number, and each encoding hands that number to a different table. The pair 11000011 10101001 is 195 followed by 169: UTF-8 reads the two together as the single letter é, Latin-1 reads them as two separate characters à and ©, and 8-bit ASCII refuses both because its numbering stops at 127. Nothing in the digits themselves says which table was used, which is why every decoder has to be told or has to guess.

One group is the wrong length, which nearly always means a digit was lost in copying. Counting groups from the left, number 6 arrived with seven digits instead of eight, and the message also gives the position in the box where that run starts so you can find it without counting by hand. The usual culprits are a chat app collapsing two spaces into one and a forwarded message that got clipped at the end of a line.

A multi-byte character has lost its opening group, which is what happens when digits are copied starting from the middle. In UTF-8 the first group of a long character begins 110, 1110 or 11110 and every group after it begins 10, so a group starting 10 with nothing in front of it cannot belong to anything. Scroll back and check you copied from the start, or switch to Latin-1, which accepts any eight digits at all and will at least show you what the bytes contain.

Yes, provided the number of digits divides evenly by the group size — 40 digits split into 5 UTF-8 characters, while 41 digits split into nothing and produce a message naming the position where the run began and how many digits are spare. The trap worth knowing is unspaced 7-bit: a string of 56 digits reads as 7 characters at eight bits each and as 8 characters at seven bits each, and both readings can look plausible. When a message matters, keep the spaces in.

Type it into the number panel underneath the translator with the menu on Binary, and 45 appears beside it along with the hexadecimal 2D. That panel adds the digits up as a number rather than looking them up as a character, which is a genuinely different question from the one at the top of the page: 01000001 is the letter A and the number 65 at the same time. The arithmetic uses BigInt, so a 500-digit binary number converts exactly instead of losing precision the way ordinary JavaScript numbers do past 2^53.

Rarely in practice, but it turns up constantly in coursework and in older telecoms material. ASCII was published in 1963 with seven bits and therefore 128 numbered slots, the highest being 127; the eighth bit on early hardware was spare and usually spent on a parity check that caught line noise. Text today is byte-aligned, so the 7-bit setting here is mostly for reading material written before the byte settled the argument.