Why do alt codes only work on a numeric keypad?

My last laptop had a numeric keypad built into the normal keyboard (so I could either use letters or numbers, but not both at the same time since they shared the same keys), and I fell in love with using alt codes. The laptop I currently use only has numbers across the top of the keyboard. It drives me crazy that I can’t use alt codes anymore. Why do they only work on a numeric keypad? What is the difference between those numbers and the ones across the top of the keyboard?

For those that don’t know, alt codes are codes that produce various symbols. You simply hold the alt key while typing a certain number on a numeric keypad to produce a given symbol. For a list of alt codes, see here.