Do computer hardware engineers write code? If so, what type?

Answer 1

Some do, some don't. Usually, you need some low-level code to get the hardware to work to the point that a regular system or application developer can use the system. Sometimes it's called "embedded code", some times it's called "firmware", and a few other names to boot.

It's usually very detailed, and often at a level below an operating system.

It is often the most fun part of the project :-)

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