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A stack is a concept in computer science that works like this:

You push value A into the stack, and it takes position 1. Then you pop the stack, and get A. If you were to push A, then B, A would be pushed into position 2, and B would be in position 1. When you pop, however, you can only get the value in position 1 (B) and A would pop to position 1. This is useful for data storage, but, expanding, you can do simplified arithmetic if you store data in positions 1 and 2, and define that the ADD command sums positions 1 and 2, erases 2, and stores the sum in 1. And so on.

A software stack is a stack that is implemented in the software of a computer: A large series of commands is given to the processor that make it store data in a "stack" somewhere in memory, and are usually sequential.

Pros: Simple to implement.

Cons: Slow and resource consuming.

A hardware stack is a series of memory units, often built into the processor, that quite literally are a stack. The only way to store data in them is to push, and the only way to access it is to pop from the first position (top of the stack).

Pros: Very fast, and is useful to the processor, even when you aren't actively using it.

Cons: Has to be engineered, and is often expensive to make.

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