constructing 32 bit unsigned int in c

This is typical bit-shifting/bit-masking stuff. Here's how you set the initial value:

uint32_t value = ((part1 & 0xF) << 28)
                 | ((part2 & 0x3) << 26)
                 | ((part3 & 0xFFF) << 14)
                 | ((part4 & 0x3) << 12)
                 | (part5 & 0xFFF);

Each line uses a bitwise-AND (&) to clear the upper bits of each part so it doesn't overflow its allocated bit-width within the final value. For example, if part4 was 0xFF and you forgot the & 0x3 then the upper 6 bits of part4 (0xFC) would spill into the region for part3. Then the part is shifted (<<) to its final location and bitwise-OR'd (|) with the rest of the parts.

Some developers accomplish the same thing via bitfields but I don't recommend that approach due to potential portability issues.

Most (all?) of the other answers here so far have forgotten the bitwise-AND portion of the solution. Their answers will result in bugs if the part values ever exceed the specified bit width.

If you want to update a particular portion of the value, you'll need some more bit-masking via bitwise-AND and bitwise-OR. For example, to update part4 you'd do this:

value &= ~(0x3 << 12);  /* Clear the part4 region */
value |= (part4 & 0x3) << 12;    /* Set the part4 region to the new value */

That first line is a little tricky if you're new to bitwork in C. It says take 0x3 and shift it by 12 (result = 0x00003000), perform a bitwise-complement (result = 0xFFFFCFFF), and set value equal to itself bitwise-AND'd with that result. That's how you clear the part4 region of the value... because you're bitwise-AND'ing that region with zero the result is that region is now zero.

The second line sets the zeroed part4 region to the new value, just like we did above when setting the initial value.