Yes of course you can. And actually, there are infinitely many that can be designed and built that haven't been built yet. Just like there are still many many PCBs that no one has built yet, because in essence a custom IC, generally known as an ASIC (and the most popular circuit technology today on that ASIC is called CMOS VLSI), is a tiny PCB. What you design there is literally a tiny circuit board with tiny transistors, resistors, capacitors and connecting wires that then gets built by etching silicon and depositing materials on top, etching these again etc, pretty much like an electronic layer cake.

Problem there is the setup costs are incredibly high, and the software you need costs in the millions per year per seat. If you're affiliated with a university, you can get the software cheaper (thousands instead of millions) and there are waver pooling programs that bring down setup costs, just like PCB pooling programs bring down costs per PCB if you need only small numbers. But even then you're still looking at something between $50k and $100k. But the actual production cost is very low. You could say the first one costs $100k, but the second, third, fouth, ... one cost $0.10 each.

The process is complicated, much more complicated than a large regular PCB, and you have to observe a large number of design constraints, and you have exactly one shot to get it right. If anything goes wrong, anything at all, you just burned $100k and probably just lost your job. That's why in ASIC design generally everything is double and triple checked at every single of the design steps. And I do mean literally triple-checked, with multiple different software packages from multiple vendors and by multiple engineers.

If you want to know how this works in detail, look at "VLSI CMOS Design, A circuits and systems perspective, 4th edition", by Neil Weste and David Harris, which you can get at the book store of your least distrust (here for instance), or find as decentralized backup copy pdf via your favorite search engine...

Now, for simple requirements like yours, there is actually something easier and much cheaper, called an FPGA, or a CPLD. They're both the same thing, but an FPGA has more design elements. CPLDs have dozens or hundreds, FPGAs have tens of thousands to millions.

Now what are these? Instead of building the circuit from scratch like in an ASIC by etching silicon, what you get in them are predefined logic blocks and a switchable interconnect fabric between them premade for you. The logic blocks usually consist of one look-up table (which can simulate a number of connected and, or, xor and not gates), and flipflops as storage elements. Often they also have a few specialized elements that are needed often and that would otherwise use up a large number of logic elements. Popular specialized elements are SRAM, and DSP ALUs (math units optimized for signal processing). The larger ones also have entire arm cores next to the FPGA fabric that you can run a regular linux on (or whatever you want to run on it, it's a regular CPU) that has connections into the programmable logic.

It's essentially a huge Lego set of logic elements. These are much cheaper than ASICs (you can get simple ones for less than $10 a piece, even without volume rebates), and they're much easier to program for (but still not trivial). While for an ASIC, you need an actual IC foundry (i.e. a factory/company that makes the ICs), an FPGA is generic, and you program it with a bitstream, which in turn is generated from your desciption of the hardware you want inside, which is written in either VHDL or Verilog. That's actually the same languages you also write the hardware for ASICs in. (They're both equally good/bad, so pick one. I would recommend VHDL, but just like with vi and emacs, if you ask 100 people, you get 250 different recommendations and reasonings there. So pick one, start with it, and learn the other one later once you know the basics. Ultimately you'll need to know both).

For a first glance into this area of electronics, have a look at this tutorial from Intel/Altera (Intel's FPGA division, formerly Altera, is one of the big three FPGA makers, the other two being Xilinx and Lattice Semiconductors). As cheap first hardware to go along with this and get your feet wet, have a look at the MAX1000 board from Arrow Electronics/Trenz Electronics, which costs about $30, give or take. That's about as low as you can get with FPGA boards, price-wise. Sadly there isn't an "FPGA Arduino" yet, but I actually think adafruit is actively working on that right now, so that may actually happen very soon.

Either way, feel free to ask questions if you have any. Good luck and have fun!

1. Is Python good to start? And is it difficult? It is not difficult to start, however biggest issue I had when starting out programming with this language is getting the syntax right, the formatting on it tends to be fussy compared to other languages and it can somewhat be tedious to code in Windows 10 compared to other languages.
   
2. Does programming require a lot of "intelligence"? As someone who studies intelligence, the term intelligence can be very subjective, here would help to break down components, you have intelligence quota and emotional quota, in my opinion I believe you have to have a strong balance of emotion and actual intelligence in order to reach the arkasia effect / satisfactory reward to avoid procrastination and such. This is a working hypothesis of mine however. Then you could say as well, being good with math would be beneficial so to be intelligent in mathematics area would help you a lot. It is a really hard thing to define and I have tried to narrow it down best as I can in terms of programming. Problem solving intelligence would also be a good one.
   
3. Do you know quality youtubers that make good videos about it?
   
   ​
   
   https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
   
   https://www.youtube.com/channel/UC9-y-6csu5WGm29I7JiwpnA
   
   https://www.youtube.com/channel/UCr-5TdGkKszdbboXXsFZJTQ
   
   https://www.youtube.com/channel/UClcE-kVhqyiHCcjYwcpfj9w
   
   https://www.youtube.com/channel/UCeQhZOvNKSBRU0Mdg7V44wA
   
   https://www.youtube.com/channel/UCMy_zy0dw4fCfs2cL7UPBQA
   
   https://www.youtube.com/channel/UCxzC4EngIsMrPmbm6Nxvb-A
   
   https://www.youtube.com/channel/UCYaNsGvyvIupxpecr4rZY9A
   
   
   
   
   
4. Do you know any books that can help me?
   
   - Exercises for programmers: https://www.amazon.fr/dp/1680501224/ref=cm_sw_r_tw_dp_U_x_vAMPCbVG5MBP5
   
   - Daily coding problem: https://www.amazon.fr/dp/1793296634/ref=cm_sw_r_tw_dp_U_x_2AMPCbT6F7Q4S
   
   - Any book on 'programming logic and design' however I like the book by Tony Gaddis titled 'starting out with programming logic and design.': https://www.amazon.fr/dp/0134801156/ref=cm_sw_r_tw_dp_U_x_2BMPCbEG3XSET
   
   
5. Do I have to learn a new language for programming (in the sense or maybe there is a country that works very well in there and that could help me on that)?
   
   There are some variants of programming languages in other languages, however I find pretty much every country will usually code in English with the exceptions mainly being in Russia and China who I believe have strongly developed programming languages in there native languages, not to sure about French, see here for more information: https://en.wikipedia.org/wiki/Non-English-based_programming_languages
   
   
6. What are the most useful programming languages for you?
   
   The ones I use in my work mostly is usually Python and Matlab for more scientific like stuff, but I also use C and C++ a lot.
   
   
7. What are the best programming languages to start? In my opinion, anything that originated from C is good, I personally started with C++ and Scratch MIT (although many would argue this is not really programming but its good to learn the very basics) and this has allowed me to learn other languages a lot easier, I started around 2012 and I now know how to code kinda decently in about 10 languages or so.

Hmmmm I don't consider myself an authority on VHDL/Verilog but I can try and answer your questions.

1. Is it relevant to learn VHDL? It really depends on your interest and goals. EE is such a wide topic that it can easily be irrelevant to your future occupation. Personally, I wouldn't treat learning VHDL as a career goal but more of a learning experience. I find VHDL to be amazing when it comes to digital design and understanding how a system works. I'm not entirely sure with which one is better but I would go with VHDL because there seems to be more resources dedicated to it (but I could be wrong).
   
   
2. If you're interested in learning VHDL I recommend Circuit Design and Simulation with VHDL
   Here's a link to a pdf, but I do advice buying the book. https://is.muni.cz/el/1433/podzim2008/PV200/um/_eBook__MIT_Press_-_Circuit_Design_with_VHDL__2005_.pdf
   https://www.amazon.com/Circuit-Design-Simulation-VHDL-Press/dp/0262014335/ref=sr_1_1?ie=UTF8&qid=1469912010&sr=8-1&keywords=circuit+design+and+simulation
   
   
3. Not sure about the CPLDs vs FPGAs so I can't really help you on that. I would go with getting a FPGA though. Unfortunately, FPGAs are pretty expensive so you would probably have to shop around if you want a good deal.
   
   Hope this help! Feel free to msg me if you have any VHDL questions.

For books, my adviser seems to like: https://www.amazon.com/VHDL-Digital-Design-Frank-Vahid/dp/0470052635/ref=sr_1_11?ie=UTF8&s=books&qid=1231766888&sr=8-11.
I'm sure it has nothing to do with Frank Vahid being his old advisor... but Frank does know his stuff and his books are typically easy to follow (I have not read this book). It's obviously VHDL and not Verilog, but it's not hard to go from one language to another.

I'm currently reading through: https://www.amazon.com/gp/product/1523364025/ref=oh_aui_detailpage_o04_s03?ie=UTF8&psc=1.
It's SystemVerilog, still not Verilog, but SV is a super-set of Verilog so it still may be useful. Also, if you use SV for verification you will be happy. DPI is your friend.

Hopefully this was a little helpful.

When you start programming the FPGA, I would definitely start with SystemVerilog, there are some really good resources on it, and it is even easier to pick up than Verilog, but gets the same thing done. By and large the tools from Xilinx and Altera get the same thing done as well, but I wouldn't completely write off the Xilinx toolchain. You should also expect to spend most of your learning time at first inside of the simulator, and even when you think you know what you are doing the simulator is an invaluable tool. For learning the ins and outs of SystemVerilog, the FPGA itself is really just a way to demonstrate what you've built, 95% of the learning can happen without it. You will probably also hear a lot about synthesizable vs. non-synthesizable SystemVerilog, for that I would definitely recommend https://www.amazon.com/Logic-Design-Verification-Using-SystemVerilog/dp/1500385786 as its what Carnegie Mellon uses to start off their digital logic classes.

Edit: Also the Pynq board is a great place to start learning about SoC development, while still having high level resources like Python and Linux available should you need them for a project.
http://store.digilentinc.com/pynq-z1-python-productivity-for-zynq/

Where/how you figure this out?

By 1) getting into semiconductor processing and process design, 2) getting into device modeling, and 3) becoming an analog IC designer - and, of course, working in the semiconductor industry. In school you focus on upper division and graduate classes in these areas.

Generally you need all three to understand this area well. That's kind of how I fell into it. Leading edge analog design quickly becomes limited by the specifics of your simulation models and your specific process implementation. Usually parameters of process and device become factor in your analog circuit design and you may even adjust physical CAD layout to tweak them.

This is where SPICE models come in. Basically you keep getting new ones added to CAD systems over the last 40 years because of some corner that isn't well modeled. The simplest models (like MOS 1->3 and Gummel-Poon) worked OK for very large devices 40 years ago when SPICE was invented but process shrinks have created lots of nonidealities since (which is the nonideality? the device or the model? :-) ). Nature of the beast.

The simple fact however is that you can never get a device model to actually cover all corners of operation equally well. Such a model doesn't exist and probably never will.

Instead the reality is that you generally need fairly peaked experts extracting parameters and often even creating new models with the caveat that you always have to compromised on the model extraction accuracy to fit the particular application corner you are designing to.

So, for example, if are doing high power, you'll optimize one of the standard models for that corner and sacrifice low power accuracy or vice versa. If you are doing RF/uW devices, you make a different set of compromises than you would if you were doing digital or LF linear. In 40 years it's never become turn-key and automated - the degrees of freedom in the models generally don't properly match those of reality. Too many or too few cause problems with the extraction.

There are other areas related to SPICE model extraction that are very similar with just a small change of emphasis.

These include parametric process measurement which monitors each fabrication step using end-of-line analog testing of specialized test structures. This is more focused with manufacturing process control and device operational integrity "out the door". A side area to this is reliability testing - when with the devices fail in the field (and they will fail). Bread and butter to me. Been doing stuff in this general area for most of my career.

Some books on my shelf are the following (they are so common they are usually referred to by the author's name):

Physics of Semiconductor Devices (Sze)

MOS (Metal Oxide Semiconductor) Physics and Technology (Nicollian/Brews)


Semiconductor Device Modeling with Spice (Kielkowski)

SPICE: Practical Device Modeling (Antognetti)

Semiconductor Material and Device Characterization (Schroder)

Failure Mechanisms in Semiconductor Devices (Amerasekera/Najm)

Failure Modes And Mechanisms In Electronic Packages (Singh/Viswanadham)

You can also hang out at /r/chipdesign which is probably the closest subreddit to this area. I'm a moderator there.

Possibly one of these? They were the only books about coding/computers with the name Charles that I could find. I'm guessing you're talking about the first one. It looks like a more popular version of things, but probably all still new stuff for me, so I'll check it out!

EDIT: The second one looks really promising too. Thanks for the suggestion!

Code: The Hidden Language of Computer Hardware and Software by Charles Petzold

Fundamentals of Logic Design by Jr. Charles H. Roth & Larry L. Kinney

Fundamentals of Logic Design - Charles H. Roth Jr.

this was my Digital Electronics Design and Analysis textbook. I can definitely say that this was the most useful textbook I ever purchased for school. The class was "self-taught" and the book is written for people that are trying to learn on their own. It makes concepts really easy to understand and covers a wide range of topics including: digital components, VHDL programming, algorithm development, practical applications, etc. If you are even the least bit interested in learning anything about digital electronics, this book is excellent.

Tony Gaddis's Starting Out with Programming Logic and Design is pretty good. Pretty language-agnostic in that it uses pseudocode to illustrate programming concepts you've mentioned, plus things like program design.

-----
-----

BOOKS

Children Electronics and Electricity books:

• "Electricity for Young Makers" by de Vinck.
  
  
• "Make: Easy Electronics" by Platt. (12 experiments)
  
  
• "Electronics for Kids: Play with Simple Circuits and Experiment with Electricity!" by Dahl.
  
  
• "Electronics For Kids For Dummies" by Shamieh. (13 experiments)
  
  Newbie Electronics books:
  
  
• "Make: How to Use a Breadboard" by Ragan and Culkin. (10 experiments)
  
  
• "Make: Electronics" by Platt. (34 experiments)
  
  
• "Make: More Electronics" by Platt. (36 experiments)
  
  
• "Lessons in Electric Circuits - Volume VI - Experiments" by Kuphaldt. (free book)
  
  
• Series "Engineer's Mini-Notebook" booklets by Forrest Mims. (download archives)
  
  
• List of books about 555-series Timer ICs on Wikipedia.
  
  Basic Circuit Theory books:
  
  
• "Electrical Circuit Theory and Technology" by Bird. (download old edition)
  
  
• "Introductory Circuit Analysis" by Boylestad. (download old edition)
  
  
• Series "Lessons In Electric Circuits" by Kuphaldt. (free books)
  
  
• List of books about Diodes, Transistors on Wikipedia.
  
  Analog Design books:
  
  
• "Microelectronic Circuits" by Sedra and Smith. (download old edition)
  
  
• "Electronic Devices and Circuit Theory" by Boylestad and Nashelsky. (download old edition)
  
  
• List of books about Operational Amplifier (OpAmp) ICs on Wikipedia.
  
  
• List of books about LM-series Analog Linear ICs on Wikipedia.
  
  Digital Design books:
  
  
• "Digital Fundamentals" by Floyd. (download old edition)
  
  
• "Digital Design: Principles and Practices" by Wakerly. (download old edition)
  
  
• "Digital Design: with Introduction to Verilog, VHDL, SystemVerilog" by Mano and Ciletti. (download old edition)
  
  
• "Digital Design and Computer Architecture" by Harris and Harris.
  (download old edition)
  
  
• List of books about 7400-series TTL Digital Logic ICs on Wikipedia.
  
  
• List of books about 4000-series CMOS Digital Logic ICs on Wikipedia.
  
  Digital Signal Processing books:
  
  
• "Scientist and Engineer's Guide to Digital Signal Processing" by Smith. (download or online)
  
  Computer Design books:
  
  
• List of books about
  6502,
  6800,
  6809,
  8080,
  8085,
  Z80,
  68000,
  x86
  processors on Wikipedia.
  
  
• List of books about
  8051,
  ARM,
  AVR,
  PIC,
  RISC-V
  microcontrollers on Wikipedia.
  
  Electronics Reference books:
  
  
• "The Art of Electronics" by Horowitz and Hill. (download example chapter)
  
  
• "The Art of Electronics - The X Chapters" by Horowitz and Hill. Shipping in 2020.
  
  
• "ARRL Handbook" by various ARRL authors. (download very old edition)
  
  Historical books:
  
  
• "The Intellectual Rise In Electricity - A History" by Park Benjamin in 1895.
  
  
• "Electricity - It's History and Development" by William Durgin in 1912.
  
  
• "Bibliographical History of Electricity & Magnetism" by Paul Mottelay in 1922.
  
  
• "History of Communications Electronics in the United States Navy" by Linwood Howeth in 1963.
  
  -----
  -----
  
  

  MAGAZINES
  

  
  Current Electronics Magazines: (subscribe now)
  
  

• "Circuit Cellar"
  
  
• "Elektor"
  
  
• "Everyday Practical Electronics"
  
  
• "Nuts & Volts"
  
  Historical Electronics Magazines: (archives)
  
  
• "Electronics Today"
  
  
• "Everyday Electronics"
  
  
• "Popular Electronics"
  
  
• "Practical Electronics"
  
  
• "Radio Electronics"
  
  Historical Computer Magazines: (archives)
  
  
• "Byte" - 2nd group
  
  
• "Dr Dobb's Journal"
  
  
• "Interface Age"
  
  

• "Kilobaud"
  
  -----
  

Well, you need to learn some HDL(s) first, VHDL or Verilog for exemple. I would recommend you to pick up a reference book like the Volnei Pedroni VHDL, or Pong. P. Chu.


http://www.amazon.com.br/Circuit-Design-Simulation-Volnei-Pedroni/dp/0262014335

http://www.amazon.com/FPGA-Prototyping-VHDL-Examples-Spartan-3/dp/0470185317/ref=asap_bc?ie=UTF8


And you can practice here: http://www.edaplayground.com/ without having to download any tool. After you stick to the HDL methodology, you start to think about prototyping, placing, routing, layout on a physical FPGA. I would recommend you to take a look in hardware verification and testbench design, depending on what you're implement it will be crucial to have a robust verification enviroment to avoid huge debugging efforts and lots of headaches.

Syllabus looks pretty standard for a digital electronics course. Sedra/Smith's book is also pretty popular among integrated circuit designers. What exactly are you having problem with? Circuits with transistors? CMOS devices? What circuit based classes have you taken before this?

I've taken a similar class called VLSI design and this is the book we used in it. Explanations in it could be a little easier for you than Sedra/Smith.

Ya I know that the Gray, Meyer, and Hurst book is pretty good. I'm not sure if the Rabaey is the book for me, I'll give it a try though. I was thinking about using this book for learning digital CMOS circuits but I'll see which one I like better.

1. Read those two books and understand them. Now you can calculate the closed-loop gain of any opamp circuit.
   
   
2. Find an Opamp Circuit Collection, either in manufacturer's Application Notes or in books. ONE , TWO , THREE , FOUR , FIVE , SIX . Do a table lookup: find your circuit in their collection. Then read their analysis, including their calculation of its gain. Then decide whether you trust them.
   
   
3. Find an EE who has taken and passed a couple of courses on circuit design with opamps. Pay her to analyze your circuit and explain it to you.

There are a million solutions to the Fermi Paradox, in my mind it really isn't a paradox at all. If you're interested to read more deeply into this subject, and to consider more possibilities as to why the aliens are not here, I would HIGHLY recommend this book. It's one of the most interesting pieces of non fiction I have ever read:

http://www.amazon.com/Contact-Alien-Civilizations-Encountering-Extraterrestrials/dp/1441921079/ref=sr_1_1?ie=UTF8&qid=1370528739&sr=8-1&keywords=contact+with+alien+civilizations

Agree. I picked up on that from the intro to GEB, stopped reading GEB, and decided to get a better understanding of Gödel's proof by reading the book Hofstadter says introduced him to Gödel - Gödel's Proof, by Ernest Nagel and James R. Newman. I recommend it as a very approachable introduction to Gödel's incompleteness theorems. Even now I can recall moments reading that little book where I'd get a big smile on my face as the force of his argument and conclusion would bear down on me. What Gödel did is nothing short of mind blowing.

After that, if you want more, then go to Gödel's Incompleteness Theorems by Raymond M. Smullyan (You'll want to buy this one used). This one is a much more technical, though still approachable if you're prepared at an undergrad level, guide through to Gödel's conclusions. You should go into it with an undergrad level of fluency in propositional and predicate logic.

You can read GEB without all that, certainly without the second book, but I've found it a better experience having more familiarity with Gödel as I work through it.

Hello, I tried clicking the weekly questions link on the sidebar and I was directed here. Not really a purchase help post but I'm really interested in learning the theory behind audio and I don't know where to begin. I took Physics II last year but I wasn't interested in any of it then and I barely remember anything. I still do have access to my Physics book in which they have 2 chapters about sound and waves so I plan on reading that.

I understand what amps, preamps, dacs, different kinds of headphones, and whatnot but not really the theories. So since I have next to 0 knowledge about this, I would like to ask what readings I should go through if I want to learn all this although I'm mainly interested in headphones. Someone recommended Op Amps for Everyone but I'm kind of intimidated with it. I'm not so sure.

Thanks, any input would be great.

This Book was the text for my Circuits I course. It was also my sister's text, and I think even my Dad had a copy from way back.

I'm sure there are others, but this one works pretty well I think. If you're looking for a book.

Book recommendations:

https://www.amazon.com/Starting-Programming-Design-Computer-Science/dp/0134801156/ref=mp_s_a_1_1?keywords=tony+gaddis+logic&qid=1568820550&s=gateway&sr=8-1

Cheaper older editions of this book would be just as good, basically the same content. It's a college book so they just make small insignificant changes to keep charging top price (hint: google older edition PDFs). The book is good though.


https://www.amazon.com/gp/aw/d/B07SZPTZ1K/ref=tmm_kin_title_0?ie=UTF8&qid=1568820681&sr=8-1-spons

This book would help you in writing flowcharts and then translating to an actual programming language (python) back and forth. I highly recommend it. There are tons of examples, practice problems, quizzes, etc. with answer keys all on the guy's website.

The authors are a married couple who used to work in software engineering and now are actual CS high school teachers. In other words they actually use teaching theory in their instruction which is rare in tech books, the spiral approach to be exact (https://en.m.wikipedia.org/wiki/Spiral_approach).

Depends very much where you start. "FPGA development" is a pretty broad field touching electronic and digital design, system architecture, hardware design languages, toolchains, simulation, testing, design synthesis, timing analysis and more. I'm not aware of "one" book covering everything. Here are some popular titles from entry level to advanced with a decent coverage of the mentioned topics:

https://www.amazon.com/Programming-FPGAs-Getting-Started-Verilog/dp/125964376X

https://www.amazon.com/Fundamentals-Digital-Logic-Verilog-Design/dp/0073380547

https://www.amazon.com/Advanced-FPGA-Design-Architecture-Implementation/dp/0470054379

If you intend on getting up to higher circuit analysis it’s going to require a bit more math. To be able to understand microelectronics/amplification/filtering, you’ll need to learn a bit about differential equations and linear algebra. You can check out this great circuits book (https://www.amazon.com/Analysis-Design-Linear-Circuits/dp/1118065581/ref=nodl_) and once you’ve gotten through that, you can dig deeper into integrated circuits with this book (http://global.oup.com/us/companion.websites/umbrella/sedrasmith/). Good luck!

I would consider reading this book (https://www.amazon.com/Starting-Out-Programming-Logic-Design/dp/0133985075). It is independent of any language and teaches you the basics of programming using pseudo-code. If you do decide to learn a particular language, you could write out the pseudo-code in that language to help you learn that way.
edit:
find an earlier edition to save money. maybe 2nd edition if you can find it.

Our Logic class was entirely self taught, our book was this. It seemed to be good enough, and I am sure getting a much older edition wouldn't change much at all.

This book is awesome: https://www.amazon.com/Analysis-Design-Linear-Circuits/dp/1118065581

You might want to start with a book on logic and program design rather than focus on a specific language. Some of it you will have already picked up implicitly, but it's a good place to start none the less. There are pdfs of this book floating around the web.

Well, if you want to become an engineer, you'll need to go to college. After you get your prereqs out of the way, the first courses you'll take will be something like Circuits 1 and 2, covering RLC circuits and basic transistors, opamps, etc., and a digital course covering logic gates, flip-flops, etc. Later on, you'll get into Fourier and Laplace transforms, more analog and digital, and elective subjects based on your specialization.

Typical books:

Circuits: http://www.amazon.com/Fundamentals-Electric-Circuits-Charles-Alexander/dp/0077263197

Digital Design: http://www.amazon.com/Fundamentals-Logic-Design-Companion-CD-ROM/dp/0495471690

Goedel's Incompleteness Theorems, by Raymond Smullyan.

From the preface:
> [intended] for the general mathematician, philosopher, computer scientist and any other curious reader who has at least a nodding acquaintance with the symbolism of first-order logic..and who can recognize the logical validity of a few elementary formulas.

I'm guessing most of the people on /r/math meet that description and more. If you want a general introduction to mathematical logic and computation, you should read Computability and Logic by George Boolos. If you can read Boolos, you can probably read Smullyan, and if you read them both you should emerge with some understanding of incompleteness.

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Thanks!

Once you're up and running and have a few designs working you might find this book useful:

http://www.amazon.com/Advanced-FPGA-Design-Architecture-Implementation/dp/0470054379

You (meaning OP) may find useful either Smullyan's book http://www.amazon.com/Godels-Incompleteness-Theorems-Oxford-Guides/dp/0195046722 or Hofstadter's http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 .

EDA Playground (simulate VHDL/Verilog online)
https://www.edaplayground.com/
Check youtube for usage tutorials.

Vendor Materials for General VHDL/VERILOG & FPGA Concepts
Altera Intel https://www.altera.com/support/training/university/materials.html
Xilinx https://www.xilinx.com/support/university/vivado/vivado-teaching-material/hdl-design.html

Past Recommendations
https://www.reddit.com/r/ECE/comments/50tlkl/fpga_bookresource_reccomendations/d7c08i8/
https://www.reddit.com/r/ECE/comments/451e7z/can_fpga_be_self_taught/czusnlc/

I recently picked up two books to refresh my VHDL knowledge. The first one appears to give a good introductory rundown.
https://www.amazon.com/Circuit-Design-Simulation-VHDL-Press/dp/0262014335/
https://www.amazon.com/Effective-Coding-VHDL-Principles-Practice/dp/0262034220/

Found my old textbook: https://www.amazon.com/Fundamentals-Logic-Design-Companion-CD-ROM/dp/0495471690/ref=sr_1_2?ie=UTF8&qid=1478084681&sr=8-2&keywords=fundamentals+of+logic+design

There might be better ones out there, but this did the job for me.

I found the book:

http://www.amazon.ca/Fundamentals-Logic-Design-Companion-CD/dp/0495471690/ref=sr_1_1?ie=UTF8&qid=1254258981&sr=8-1

https://www.amazon.com/Starting-Programming-Design-Computer-Science/dp/0134801156/

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