What is the purpose behind having the num lock key off during startup?
This may have historic reasons. When the NumLock key was invented, there were no other arrow keys on the keyboard, so defaulting it to off made sense.
Nowadays, it's a matter of personal preference. Some people (me included) could not live without the numeric keypad; other never use it. But since you can adjust the setting, it doesn't really matter to what it defaults.
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Shinrai
This is purely a preference thing - most modern systems should tolerate it either being on or off. Indeed, most systems have the default for this as a configuration option in the BIOS.
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davidgo
No, this would be convention only. Some bioses (at least historically) even had the option to set this. As you can boot even without a keyboard (or a USB or PS2 keyboard if the PC supports it), it would be safe to assume that, technically its a trivial question.
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Hennes
On desktops it is a matter of preference. Either you boot with num-lock on and use the numberpad, or you boot with num-lock off and use the cursors on it.
Since most 'modern' keyboards now come with a dedicated cursor and a 6 key PgUp/Down/Home/End/Del/Insert block the choice is no longer as important as it used to be.
On laptops it is a different story. Many laptops an internal keyboard with no numpad. Turning numpad on disables a lot of keys on those keyboards, and maps them to numbers.