Minimum GCC Version Likely to Jump from 3.2 to 4.8

The question of the earliest GCC compiler version to support for building the Linux kernel comes up periodically. The ideal would be for Linux to compile under all GCC versions, because you never know what kind of system someone is running. Maybe their company's security team has to approve all software upgrades for their highly sensitive devices, and GCC is low on that list. Maybe they need to save as much space as possible, and recent versions of GCC are too big. There are all sorts of reasons why someone might be stuck with old software.