I have found that once you work for a company where you have to implement everything in its raw form using the raw language and raw logic, you really have to know what you're doing and knowing some basic/medium programming and having some algebra knowledge doesn't cut it (unlike some people think).

I've been at two sides of the coin: I worked for a company that had everything in place, a framework that handled all edge cases and what not and I just had to focus on user stories, but I also worked for a company where I had to do everything manually.

For example, at the latter company I had to know Discrete Mathematics; truth tables to their most convoluted and disgusting form, having to be able to apply this on a late Friday night with a headache and lack of food and sleep with the PM stressing out.
I've had to deal with NOT AND OR AND OR AND OR AND branches or whatever, where an OR behaves like an AND and if you want a value between an AND AND and an OR, you'd have to do a NOT OR.. to think about latches, all in my head, sigh, anyway, within limited time constraints, without even having time to write tests, having to make sure that everything checks out while the client is breathing down my neck. Yeah, not such fun times.

I'm happy for those of you who can just write some moderately difficult logic but you don't have to break your head over doing everything manually, as if you're in the coding stone age and nothing is taken care of.
Companies like these make me want to run away.

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    The Quine-McClusky algorithm can be quite useful for such a case.
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    Use a SAT/SMT solver to check your logic, I do that whenever I don't fully trust my thinking. There are a lot of really good open source ones like Yices2, CVC4, Microsoft Z3 etc.
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