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Unless you can explain when firmware is not software (which you can't) - you are barking up you own private tree of faulty logic.

Firmware
From Wikipedia, the free encyclopedia.
In computing, firmware is software that is embedded in a hardware device, that allows reading and executing the software, but does not allow modification, e.g., writing or deleting data by an end user.
Examples of firmware include:
- the BIOS found in personal computers,
- Open Firmware, used in Apple Macintosh computers,
- the computer program in a read-only memory (ROM) integrated circuit (A hardware configuration is usually used to represent the software.),
- the erasable programmable read-only memory (EPROM) chip, whose program may be modified by special external hardware, but not by an application program.
Source: from Federal Standard 1037C and from MIL-STD-188

"Embedded in hardware" and "A hardware configuration is usually used to represent the software"...

The point that started all this is that COMPAQ took the HARD BURNED, HARD-WIRED ROM out of a IBM-PC and reverse engineered the OUTPUT of that piece of hardware by determining what it did and creating a new code that did the same thing... and then installed it in their own piece of hardware. The ROM chip in the IBM-PC that contained the BIOS was the only not-off-the-shelf component in the computer... and it was what kept all other completely identical assemblies of hardwarre and software from operating identically to an IBM-PC.

The point that started all this is that COMPAQ took the HARD BURNED, HARD-WIRED ROM out of a IBM-PC and reverse engineered the OUTPUT of that piece of hardware by determining what it did and creating a new code that did the same thing... and then installed it in their own piece of hardware.

Actually none of that is true - it is pretty obvious you are blow-hard that really does not understand the subject. Compaq did not take the bios out of the machine. Compaq used two groups of software engineers - one that had access to the source code for the bios (software) and one that did not and wrote a bios (software) that functioned like the IBM bios (by observing the functioning of an IBM PC). Compaq reverse-engineer software, not hardware. The bios software is written to ROM chips - all software is written to some form of hardware.

Let's repeat the first line of the definition:

In computing, firmware is software that is embedded in a hardware device, that allows reading and executing the software, but does not allow modification, e.g., writing or deleting data by an end user.

Now will you stop trying to claim firmware<>software. The only difference between the subgroup firmware and the superset software is firmware is read-only - all software is contained on a hardware device.

Last example:

Draw circle the size of a diner plate.

That is group A

Draw a circle inside of the group A circle the size of a quarter.

That is group B

The area inside of group B is 100% group A

B=A

The area inside of group A is not 100% of group B - only a small percent of A is within group B

A<>B

Group A is software and group B is firmware.