What happens when you truncate an integer to a smaller type?

The high bits are simply dropped and the remaining low bits are reinterpreted — for unsigned values this is exactly the value mod 2^w (where w is the new, smaller width).

Truncation is the inverse of expansion: instead of adding high bits, you discard them, keeping only the low w bits.

Example: a 32-bit int truncated to a 16-bit short:

0x12345678  ->  0x5678   (keep only the low 16 bits)
            =   22136     (as unsigned short)

Rules:

• Unsigned → smaller unsigned: result = original mod 2^w (pure modular reduction).
• Signed → smaller signed: keep the low w bits, then reinterpret them in the new width — so the result's sign comes from the new MSB, not the old one. This is "similar to mod" but the value can flip sign.
• For values small enough to fit in the smaller type, truncation gives the expected (unchanged) result.

int   big   = 100000;       // 0x000186A0
short small = (short)big;    // 0x86A0 = -31072 ! (high bits lost, MSB now 1)

Tip: Expansion always preserves the value; truncation does not — it can silently change or even flip the sign once the value no longer fits.