Number Bases: Decimal, Hexadecimal, Octal

Core Idea

Computers store bits. Humans write numbers in different bases to make those bits readable. Decimal is base 10. Hexadecimal is base 16. Octal is base 8.

Why Linux Uses These Bases

• Decimal: normal counts, sizes, process ids, ports.
• Hexadecimal: byte inspection, memory, colors, hashes, binary file views.
• Octal: Unix permission shorthand such as 755 and 644.

Commands To Try

printf 'A' | xxd
printf '%d\n' 0x41
stat -c '%a %n' ~/playground 2>/dev/null || true

0x41 is hexadecimal for decimal 65, which is the ASCII byte for A. Permission mode 755 is octal: owner can read, write, execute; group and others can read and execute.

Permission Octal

read    = 4
write   = 2
execute = 1

Add them per permission triplet:

7 = 4 + 2 + 1 = rwx
6 = 4 + 2     = rw-
5 = 4     + 1 = r-x
4 = 4         = r--

Common Confusions

• 10 means different values in different bases: decimal ten, binary two, octal eight, hexadecimal sixteen.
• Hex digits continue after 9 with a through f.
• Octal permissions are compact, but symbolic modes such as u+x are often safer while learning.

Proof Check

Explain why chmod 755 script.sh gives the owner write permission but chmod 555 script.sh does not.

Docs Pointers

• Run man chmod, then read numeric mode descriptions.
• Run man xxd.
• Read Wikipedia on hexadecimal and Wikipedia on octal.