As a noun, it is the act of dealing with something through a series of steps, such as data, food, or applications. As a verb form, it describes currently performing those steps.
From *process* plus the suffix *-ing*, marking an ongoing action. It carries the Latin root idea of 'going forward through steps'.
When a computer says 'processing…', it’s doing the same basic thing your brain does when you say 'Give me a second.' Both are turning raw input into a result. We talk about 'processing emotions' now too, treating feelings like data that need time to be sorted.
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