Assignments always truncate the most significant bits and retain the LSBs. Other arithmetics operations truncate the result too, if it overflows. In that way you can extend the maths (and many other operations) for operating on big integers easily. Without truncation how can you crammed 32 bits into 8 bits?
To copy the 32-bit int into an array of 4 8-bit chars, the easiest ways is copy the whole number into the array. Another way is assign element-by-element
smallVbl[0] = bigVbl & 0xff; // the & 0xff is not really needed
smallVbl[1] = (bigVbl >> 8) & 0xff;
smallVbl[2] = (bigVbl >> 16) & 0xff;
smallVbl[3] = (bigVbl >> 24) & 0xff;