What runs after the computer completes initial hardware error checks?

Once the computer completes its initial hardware error checks, it runs the firmware or BIOS. This software is embedded into the computer's hardware and is responsible for initializing and testing the hardware components during the boot process. The firmware executes a series of checks, often referred to as POST (Power-On Self-Test), to ensure that necessary hardware components are functioning correctly before handing control over to the operating system.

After the POST is completed successfully, the BIOS then loads the bootloader from the storage device, which initiates the loading of the operating system. This process is crucial because if any hardware issues are detected during the initial checks, the BIOS can prevent further booting, thus avoiding potential damage or data corruption.

The other options refer to different stages or components in the computer system. The operating system runs later in the sequence after the BIOS has done its job. Application software runs even later, requiring an already functional operating system to operate. The network adapter, while important for network connectivity, is not a step in the booting process but rather a component that is initialized and tested during the BIOS checks. Thus, the role of the firmware or BIOS as the primary software running immediately after the hardware error checks positions it correctly as the answer.