How do computer's work?

This still baffles me. I've watched a few documentaries about computers and computing. Yes, I've gotten some information like history and the basics: user inputs, then the computer processes it, and then it outputs. But how does a processor process information? How did computers work before CPU's?
If anyone can point me in the right direction to some in-depth material it would be much appreciated

The things that are getting past you in all this have to do with time and complexity. You are not talking about calculators any more.
Complexity:
In showing a text document consisting of only the letter A on the screen, we must take into account:
window size
window magnification
page size
top margin
side margin
paragraph spacing
paragraph indent
tab settings {left center right decimal}
text justification {left center right fully-justified}
font
size
style {bold italic underline outline strikethrough ...}
To save that document we must consider
document name
disk file name
disk file location
disk file extent
whether the file is contiguous or has additional extents
whether the file is exclusively accessed, or shared.
These lists are greatly abbreviated. There are many, many, many more items that are actually considered. For example, the Mac also supports right-to left writing systems like Arabic, and systems where more that one byte is used to form characters like Japanese.
Each of these items has routines and subroutines. They also make calls to standard Library routines that provide commonly used functions. Each of these items may have routines that go on from a few to a few dozen pages of code. And make calls to Library routines that also extend for a few pages to a few dozen pages of code EACH.
The sizes of code I have described above refer to the "Human-readable" form that programmers write in. The language used to write these routines is a higher-level language that translates one-for-many to machine instructions. One statement of C++ may produce a dozen lines of machine instructions or more.
The Textedit application, for example has 1.7MBytes of machine instructions and invariant text in it. When it opens, it reserves more than that in memory, since it must also make room for your document.
The complexity involved with what you are calling "simple" tasks is mind-boggling.
Time:
A single computer instruction executes in times on the order of a microsecond ( 0.000,001 seconds/instruction or 1,000,000 instructions a second).
To appear instantaneous, the screen must redraw in about 1/3 second or less (1/6 second is the actual threshold of perception). Whenever it does not re-draw instantly, it is because there is so much complexity in the processing that is could not complete the processing using the multiple independent processors in your machine in parallel in that time. [For four processors that would be about 1.2 million instructions in 1/3 second.]
The speed of individual operations inside your Mac, along with how many of individual operations are needed to complete what you are calling "simple" tasks is mind-boggling as well.

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