The key is not embedded in the BIOS or anywhere else. There is no key at all.
Instead when you first activate Windows 10 it records the hardware signature (a collection of your PC's hardware device ID's compressed into a numerical identifier) in MS Activation servers as entitled to a free license for the life of the PC. The ability to change hardware without triggering reactivation is explained in the post above mine.
Later when you need to reactivate or if a Genuine check is done, the hardware signature is compared to confirm that the PC is licensed for Windows 10 Upgrade.
Because many will use retail copies of Windows 7 or 8.1 to Upgrade to 10, and these licenses are entitled to migrate to other PC's, the Windows 10 Team decided that the Upgrade should likewise be able to change hardware if need be. This is a good explanation of how this is planned to be done:
How to Use Your Free Windows 10 License After Changing Your PC’s Hardware . Only OEM copies of Windows are locked to the hardware first installed upon and cannot migrate.
They also decided that the Windows 7 or 8.1 license will not be affected by the Upgrade so that you can go back to the original OS whenever you want, as long as both are not being used at the same time. To uninstall one OS to restore the other its partition should be deleted. The best way to restore an OS is to use a
System Image Backup.