I did come across that link but didn't quite understand it. If looking only at 25 | 10, does the code not run as expected because 25 is 5 digits long and 10 is 4 digits long? Is that what's meant by "two equivalent length bit designs"?
If an int is only x bytes long, but y bytes are needed for an action, it's just padded with 0's to the left. So 0b110 = 0b0110 = 0b00000110. Usually you will use either 8, 16, 32 or 64 digits/bits (char, short, int and long respectively, and 1, 2, 4 and 8 bytes long, 1 byte = 8 bits. So you'll usually align it with bytes.) However, for calculating like this removing trailing zeroes can make it more tidy, and sometimes 4 or 2 bits are used too. And bools technically only use 1 bit.