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Is this free to use?
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Does it work on a phone?
Yes. The page runs in any modern mobile browser, on iPhone and Android alike, with no app to install.
How do I read chmod 755 as bits?
Expand each digit into three bits: 7 is 111, 5 is 101, 5 is 101, giving 111101101. Read the triads as read, write, execute, so the owner gets rwx and group and others get r-x. That is exactly the permission string ls shows.
How many bits is one octal digit?
Three, covering the values 0 to 7. That direct mapping is the reason octal is still used for permission masks and for character escapes, even though hex has replaced it almost everywhere else.
Does it accept a leading zero or a 0o prefix?
Yes. A 0o or 0O prefix is stripped, and a plain leading zero, the older C convention for an octal literal, has no value so it changes nothing. 0755, 0o755 and 755 all convert to the same bits.
What is octal 777 in binary?
111111111, nine ones. It is the maximal permission mask, granting read, write and execute to owner, group and others, and it is the reason 777 is shorthand for wide-open permissions.
Can I convert a mask like 0644?
Yes. The leading zero is notation, so 0644 converts as 644 and gives 110100100. That is rw-r--r--, which is what a normal, non-executable file should carry.