Talk:Gray code
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Excess-3 or Stibitz sources
On a different note, I am searching for the earliest references defining Gray excess-3 codes in order to nail down when they were introduced and by whom. Does someone have a "really old"(tm) ref for them? --Matthiaspaul (talk) 23:29, 22 May 2020 (UTC)
- There's a 1958 patent (or [1]) mentioning Gray excess-3. Dicklyon (talk) 06:12, 23 May 2020 (UTC)
- The Swiss version of the same patent calls it a Stibitz-Gray code, so maybe that's the thing to look more for. Dicklyon (talk) 17:04, 23 May 2020 (UTC)
- 1954 Bell Laboratories Record has Stibitz Gray code, but not decimal or excess-3 as far as I can find. Dicklyon (talk) 17:10, 23 May 2020 (UTC)
- The 1957 book by Stibitz has Gray codes, and excess-3 (shifted) binary, and bi-quinary, but I don't see excess-3 Gray there. Dicklyon (talk) 17:18, 23 May 2020 (UTC)
- The 1957 book by Maurice Wilkes has "Stibitz's excess-three code". Glaser 1981 says that Edmund Berkeley says that Stibitz came up with it in 1939. Aspray 1990 also talks about it in Stibitz's relay-based "Complex Computer". Sounds like it predates Gray? Dicklyon (talk) 17:28, 23 May 2020 (UTC)
- The George Stibitz article links his 1941 patent which describes a code: "A feature of the invention. is the use of a four place, permutation code for representing the digits of the decimal system characterized by the fact that the code for each such digit is the inverse of the code of the nine's complement thereof." But from Table 1 I'd say it's an ordinary binary excess-3 code, not a Gray excess-3, I guess I was mistaken in thinking that the Wilkes book was on the right track for the Gray variant. Dicklyon (talk) 17:41, 23 May 2020 (UTC)
- So none of these before the 1956/58 patent is what you're looking for, I guess. Dicklyon (talk) 17:47, 23 May 2020 (UTC)
- And there's another patent filed in 1956 with Turvey and others at ITT that doesn't name the code but uses an excess-3 Gray. I wonder if these guys invented it and applied the two names they combined, Gray for the reflected binary property and Stibitz for the excess-3 (applied the names in the Swiss version). Dicklyon (talk) 17:57, 23 May 2020 (UTC)
- This 1963-filed patent cites the one above and calls it a Gray excess-3 code. I haven't look at everything else it cites. Dicklyon (talk) 18:08, 23 May 2020 (UTC)
- OK, I checked their other 2 cited patents, and this 1954-filed UK patent has decimal Gray codes in 5 variants, probably one of which is excess 3. They prefer their "Example II" code, but it's not clear to me if that's excess-3. Dicklyon (talk) 18:19, 23 May 2020 (UTC)
Bottom line, I think, is this: some people adapted Gray code to "excess 3" for decimal use. They noticed Stibitz had done excess-3 for regular binary. So they combined the names. Why this show up in the Swiss version, and not the US version, of the Turvey patent is hard to fathom. Perhaps the Swiss examiner asked them to cite Stibitz. There's also a german version, with "Stibitz-Gray-Kode (Excess-3-Kode); maybe we need to search the Kode spelling more. Dicklyon (talk) 23:25, 24 May 2020 (UTC)
Knuth also points out that Stibitz had a Gray code already in this 1941-filed patent. But I see no connection to the excess-3 Gray there. Dicklyon (talk) 23:31, 24 May 2020 (UTC)
Proposal: Rotate table in "Related codes"
Two years ago, in an attempt to keep the encoding examples in § Related codes from blowing out beyond the page width, I moved the (IMHO excessive, but that's editorializing) citations out of the table headings into a separate row below the inner tables. That even worked, for a time. But, in the intervening two years, more and more variations have been added and the total width has only grown. As a result, we're right back where we started.
Since the smart money is on that trend inevitably continuing, the list of variations (and therefore the table width) will only grow. However, the list of decimal digits is not likely to grow, so I'm going to propose a solution that embraces these dual realities: Rotating the table. The result may not look familiar, and won't conform to "normal" tabular representations of Gray codes, but it's the only format that's able to handle being expanded with an indeterminate number of alternative representations. Tables can grow indefinitely in the vertical direction; not so horizontally.
So I propose this for the revised format:. It's still wider than I'd like, but at least it won't grow any wider. (Well... except for the slight increase that will be caused by some of the longer names, when all of the rows are added.)
| Decimal 0 | Decimal 1 | Decimal 2 | Decimal 3 | Decimal 4 | Decimal 5 | Decimal 6 | Decimal 7 | Decimal 8 | Decimal 9 | ||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 | 3 | 2 | 1 | ||||||||||||
| Gray | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | |||||||||||
| Paul | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | |||||||||||
| Glixon | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | |||||||||||
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Obviously, all of the currently-represented codes would be transferred. I just didn't feel like possibly wasting my time transferring all of them, so first I'm seeking consensus regarding the basic concept. That being said, the conversion is fairly easy because the table code turns out to be surprisingly similar to the current tables' source: each code's row is exactly the same as the previous table's content for that code, but with all of the row separators removed. The only other change required when adding row(s) is to increase the rowspan= value on the cells that separate each heading in the second row. Thoughts? -- FeRDNYC (talk) 18:06, 6 December 2020 (UTC)
- I forgot to add, for an even better fit with the site template, this could even be split into two sections — there's no reason the digits 0 – 9 have to all be displayed side-by-side, the table could easily be chopped in half and laid out as a table for the digits 0 – 4, then a second table below covering 5 – 9. -- FeRDNYC (talk) 06:27, 12 December 2020 (UTC)
Baudot
Can Baudot's use of reflected binary codes be explained, or even verified? What I find in sources don't show any Gray-like code, nor how we might have used them. Dicklyon (talk) 01:33, 19 December 2020 (UTC)