Every processor has a certain set of operations that it’s hardwired to perform – these operations are known as the processor’s “instruction set”. Internally these instructions are referred to by binary numbers because at the end of the day that’s all a computer is really able to work with. For example, 0011 might be the operation code for addition, 0100 might be the operation for subtraction, etc.
The problem is that referencing everything as a binary address like that is pretty tedious for humans and prone to error. So clever people started making human readable abbreviations for popular instruction sets – 0011 got abbreviated to ADD, 0100 got abbreviated to SUB, etc.
Then people wrote programs called “assemblers” that could take those abbreviations and automatically translate them in to the corresponding binary. And hence the concept of “assembly language” was born.
ADDENDUM: If you want an easy to follow step-by-step example of how a computer actually executes commands like this look up the “Little Man Computer” on Wikipedia.
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