Everything is stored as bits (each 0 or 1); the same bits mean different things depending on how they're interpreted. Integers use two encodings — unsigned and two's complement (signed).

A bit is the fundamental unit — physically just a voltage that's "low" (0) or "high" (1). On their own, bits carry no meaning; an encoding assigns meaning to a pattern.

(Real numbers use a third family, floating point — base-2 scientific notation — but this topic focuses on the two integer encodings above.)

Why these integer encodings?

• Unsigned is the simplest — just count in binary — but it can't represent negatives.
• Two's complement handles negatives so that the same addition circuit works for both signed and unsigned values.

The key insight: Everything is bits - the pattern 11111111 is:

• 255 if interpreted as unsigned (8-bit)
• -1 if interpreted as two's complement
• Part of a float if interpreted as floating point

Why this matters:

• The bits don't "know" what they represent
• The TYPE in your code tells the CPU how to interpret them
• Bugs happen when you interpret bits with the wrong type!

Each base is positional; the key shortcut is that one hex digit equals exactly four bits, so you can convert hex↔binary in 4-bit groups.

Conversion shortcuts:

• Binary → Hex: Group 4 bits, convert each group
• Hex → Binary: Expand each hex digit to 4 bits
• 0xFA1D37B = 1111 1010 0001 1101 0011 0111 1011

Tip: Each hex digit = exactly 4 bits. Memorize A=10, B=11, C=12, D=13, E=14, F=15.

Go deeper:

• Hexadecimal (Wikipedia) — the base-16 system and its 4-bits-per-digit relationship to binary.