Code: Alternative 10s

In one line: ten is just one choice — count in eights, fours or twos and the same place-value rules apply, and binary is the one electricity loves.

Companion to: Charles Petzold, Code (2nd edition), chapter 10.

Place values by base

• Base to decimal: multiply each digit by its place value, then add.
• Decimal to base: divide by the base repeatedly and read the remainders from bottom to top.
• One octal digit = three bits, so converting between octal and binary is just grouping.

Binary is the natural fit

Binary needs only two states — off/on, open/closed, 0/1 — exactly what switches, relays and transistors provide.

Circuits can decode a binary number into “which one of N lines is on” (a 3-to-8 decoder), or encode it back.

Octal in real life: Linux permissions

chmod 750 script.sh          # owner rwx, group r-x, others ---
stat -c '%a %A %n' script.sh # 750 -rwxr-x--- script.sh

Try it

oct(493)          # '0o755'
int('755', 8)     # 493
bin(100)          # '0b1100100'
int('1210', 4)    # 100

[Convert]::ToString(493, 8)    # 755
[Convert]::ToInt32('755', 8)   # 493

🔐 Security and IT connections

• Reading permissions fast: 777 means anyone can write, which is almost always wrong. 600 is right for private keys.

• A fourth leading digit adds special bits. 4755 is SUID: the program runs with its owner’s rights. Unusual SUID files are a classic privilege-escalation hunt:

  Copy

  find / -perm -4000 -type f 2>/dev/null

Practice drills

Key takeaways

• Place value works in every base; only the multiplier changes.
• Binary suits circuits because it needs just two states.
• Octal packs three bits per digit — which is why Linux permissions are written as 755 and 640.