Language design basics

Hihi, just wondering if anyone could supply me with a bit of knowledge
or point me in the right direction...

I'm just after some basic concepts so I can know what/how to research
it more thoroughly. I have some basic programming expertise
(specifically c++, javascript, and perl) - enough to create a *simple*
cryptanalytic bruteforce/analytic script.


1. How do you programme a programming language? ie. in assembly/
binary? --- then, how do you tell the computer that you're giving it
basic instruction?

That stems from my initial curiosity about mathematical fundamentals,
specifically:

2. How do you programme basic mathematical operators? Is it all a
matter of base conversion - and if so, mainly from two to ten and back
again, or for division possibly all kinds of screwy bases?

While I'm here, although possibly better suited to a different thread:

3. Memory vs. Processing - which is faster/ more efficient? Do I
create *possibly* huge lookup tables or compute my values each time?
Is there a general rule, or should I take levels of wizard and work it
out through memory/ cpu speeds (omg no please have mercy)? Is this
actually a valid dichotomy, or am I barking up the wrong decision
tree?

Thanks for any help.
.

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