Illuminating Gray Codes, LFSRs, K-Maps & More
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I was just thinking about the wide variety of topics I've written about over the years. This caused me to look up some of my old columns, many of which are “evergreen” in that they introduce and illuminate fundamental concepts.
As I was re-reading these, I thought: “This is interesting stuff that will be useful for a lot of folks who are just starting out in the industry or who haven’t looked at these topics for a while,” so I decided to remind everyone that these articles are still available for you to peruse and ponder.
- ASCII, EBCDIC, ISO, and Unicode
- Karnaugh Maps
- Logic: Assertion-Level
- Logic: Positive vs. Negative
- Logic: Reed-Muller
- Linear Feedback Shift Registers, Part 1
- Linear Feedback Shift Registers, Part 2
- Linear Feedback Shift Registers, Part 3
- Gray Codes, Part 1
- Gray Codes, Part 2
- Gray Codes, Part 3
- Gray Codes, Part 4
- Gray Codes, Part 5
I must admit that I'm really rather proud of some of these topics, such as generating sub-2^n Gray code count sequences and “n-ary” (non-Boolean) Gray codes. I'd really be interested to hear if any of the points I made in these articles make you say something like: “Wow, that's interesting — I never knew that!”
Also, the articles shown above are just the ones that popped into my head when I was thinking about this. If you remember any other “fundamental” or “tutorial” columns that I've written that fit into this general theme, I'd really appreciate it if you could remind me of them.
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22 thoughts on “Illuminating Gray Codes, LFSRs, K-Maps & More”
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“There are 10 kinds of people. Those who think I'm talking about binary, those who understand Gray code, and those who don't.”
“Good One!!!”
“You could also add to the list people who insist that indices start at 0, not 1.”
“Maxnnthee certainly are some gems here. I have always believed that there was a need for a course/book called “Finishing School for Newly Graduated Electrical Engineers”. I think these could be the basis.”
“MaxnnAt one point you promised a blog or a series of blogs on relays. I don't believe you ever published them. Can we look forward to it?”
“I used to hate starting at 0 — now I can't imagine doing it any other way — the only problem arises when the objects you are connecting to in the real world are numbered from '1' … then you have a graunching decision to make…”
“Why, thank you Aubrey – that's very kind of you. This stuff is a mix of what I learned in college and then additional nuggets I learned as the years went by.”
“To tell you the truth, this has been niggling on my mind — I wrote lots of notes that were to form the basis for a few articles — but then things got pushed to the back-burner.nnWhat I really need to do is (a) lay my hands on a bunch of relays and (b)
“Relays is exciting topic – especially when building primitive computer is involved. Showing basic digital blocks would be really interesting in such problem. Just a suggestion.”
“typo: instead of 'problem' I meant 'project'”
“”lot of small relays very cheaply”nnDefine “a lot” and will N.O. do, or do you envision needing changeover and multiple poles?”
“Where and when is the nearest hamfest to you?nnThere's also your friendly neighborhood electronics surplus store. Of course the most likely one went out of business as I recall…nnLook for an old PLC or other industrial control. They usually have rel
“I agree — relays are just interesting — it's a completely different way of working — I'd love to do this — it's only time (and money) that's holding me back :-)”
“I guess I could work only with single-pole (SP) normally-open (NO) relays. But given a choice I'd prefer to work with changeover relays, which I tend to thing of as the relay equivalent to a single-pole double-throw (SPDT) switch.nnFurthermore, if there
“I have six really tasty SPDT antique relays — black Bakelite base — all the working open to the elements — that I picked up from Mock Electronics before they went put of business — I might use these as the centerpiece…”
“I'll add that to my ever-growing “list of things to do” LOL”
“I was going to offer max a bunch of 24V relays (I do work in industrial interfacing), and throw in a 24V power supply. There are LED indicators, but most of the relays are the opaque orange or black ones. Sorry Max. We are going to have to wait for your i
“As I told David in an email, what I need to do (when I get a free moment) is to sit down, work out what function I wish to implement (maybe a small ALU or a small state machine) and then guestimate how many relays I'll need.nnOff the top of my head, I'm
“Max… “So, where can I get a lot of small relays very cheaply?” nnI can get you pretty much as many as you want of these:nnhttp://www.okorelays.com/oko/datasheets/47W.pdfnnOnly trouble is, they are 48Volt coils. I seem to remember offerin
“Great stuff Max, you should Write a book. Oh, sorry, you already did (and very good it is too).nnOne thing you may be able to correct. In the gray code series, all parts have a link to the next part at the end, except part 3.”
“@Elizabeth… “Look for an old PLC or other industrial control. They usually have relays on their I/O.” This is true, but they are usually 24V coil relays, Max wants 5V or 12V types. Also, as he told me in an email in response to my below post, he is
“Further to my above post, I found that most of the EA2 5V types are latching, and I can get quite a few (each unit has around 15 of them). Latching ones might be interesting. You put voltage on the coil one way to set them, and the other way to reset th