A canonical ChmodCalc mode has four octal digits. The first represents setuid, setgid, and sticky; the next three represent owner, group, and others. Each ordinary digit is the sum of read 4, write 2, and execute or search 1. This is a bit conversion, not a recommendation for what a real path should use.
Each ordinary digit owns one rwx triplet
The complete mapping is 0 = ---, 1 = --x, 2 = -w-, 3 = -wx, 4 = r--, 5 = r-x, 6 = rw-, and 7 = rwx. Therefore 0640 becomes rw-r-----: owner 6, group 4, others 0. Converting each triplet independently avoids treating 640 as decimal arithmetic.
The leading zero makes the special digit visible
ChmodCalc accepts three ordinary octal digits and canonicalizes them with special digit 0: 755 becomes 0755. Four digits expose all twelve modeled bits directly. Values outside 0000–7777, digits 8 or 9, prefixes such as 0o, signs, spaces, and extra digits are rejected rather than guessed.
A nine-character display is not chmod's full symbolic grammar
rwxr-xr-x is an ls-style complete permission display. ChmodCalc converts that snapshot to 0755. It does not parse state-changing clauses such as u+x, g-w, or u=rwx,g=rx,o=rx because relative operations require a starting mode and omitted classes can interact with umask.