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How do you generate 16-bit C code with DJGPP(GCC)?

you don't

try Turbo C or Watcom C

It can generate 16bit/32bit mixed code that will run on a 386+ machine in real mode.  The code will not run on a 286 or less.  I'm actually using this for my boot loader.  Before your 16bit code add:

__asm__ (
     ".code16    \n"
     ".code16gcc \n"
);

Then before your 32bit code add:

__asm__ (
     ".code32\n");
);

You will probably also want to turn off all alignment optimizations to avoid bogus code generation with some builds of GCC:

-falign-functions=1 -falign-jumps=1 -falign-labels=1 -falign-loops=1