Question 1

Why do we need different number bases?

Accepted Answer

Binary is the only base processors natively "understand" (0/1 = off/on). Octal appears in Linux file permissions (chmod 755). Hexadecimal is used for #RRGGBB colors, memory addresses, MAC addresses, and bytes in hex editors.

Question 2

How do I convert HEX to DEC in my head?

Accepted Answer

Each digit is multiplied by a power of 16. FF = 15×16 + 15 = 255. 1A = 1×16 + 10 = 26. For colors, #FF0000 is red (255,0,0) and #0000FF is blue. Each pair of hex digits is one byte (0–255).

Question 3

Why does HEX use A–F?

Accepted Answer

A single hex digit needs 16 values (0–15). Digits 0–9 cover only ten, so A–F stand in for 10–15. Without them you could not write a full byte compactly in just two characters.

Question 4

How do Linux permissions look in octal?

Accepted Answer

chmod 755 means 7 = rwx (owner), 5 = r-x (group), 5 = r-x (others). 7 = 4(r)+2(w)+1(x) = binary 111, and 5 = 101 = r-x. chmod 777 grants full access to everyone; chmod 644 lets everyone read but only the owner write.

Question 5

How do bitwise operations work?

Accepted Answer

AND (&): 1 only if both bits are 1. OR (|): 1 if either bit is 1. XOR (^): 1 when bits differ. NOT (~): flips every bit. Uses include network masks (192.168.1.0 AND 255.255.255.0), flags, and encryption.

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