How can a union be used to read the raw bit pattern of a float, and why doesn't a plain cast work?

Write the value through the float member, then read it back through the unsigned int member — since both share the same bytes, you get the float's exact bit pattern.

A union member overlays the same storage, so storing a float and reading an unsigned int reinterprets those 4 bytes without converting the value:

unsigned int get_bitpattern(float f) {
    union { float f; unsigned int u; } fu;
    fu.f = f;       // write the bits as a float
    return fu.u;    // read the SAME bits as an integer
}

Because no conversion happens, the compiled code is trivial — the 4 bytes are already in place:

get_bitpattern:
    movl 4(%esp), %eax   # just return the incoming 4 bytes unchanged
    ret

Result: 3.1415927410 = 01000000010010010000111111011011b = 0x40490fdb (the IEEE-754 single-precision encoding of π).

Why a cast fails: (unsigned int)f performs a value conversion — it truncates 3.14… to the integer 3 (0x00000003), throwing away the bit pattern entirely. The union reinterprets the bits; the cast converts the number. They are completely different operations.

Modern note: the strictly-portable, defined-behavior way to do this today is memcpy (or C++20 std::bit_cast); the union trick is the classic and works in practice on common compilers.

Go deeper:

• Type punning (Wikipedia) — type punning via unions versus a value-converting cast.