3 ms·

Here's I found a source for this: Stanley P. Frankel on the design of MINAC and the LGP-30 in IRE Transactions on Electronic Computers. (15 flip-flops, presenti

Here's I found a source for this: Stanley P. Frankel on the design of MINAC and the LGP-30 in IRE Transactions on Electronic Computers. (15 flip-flops, presenting both normal and inverted output to a logical network made of resistors and crystal diodes, providing basic monotonic Boolean functions like And, Or, and Xor.) Stanley P. Frankel, “The Logical Design of a Simple General Purpose Computer” in: IRE Transactions on Electronic Computers, March 1957, pp. 5 [1] [1] https://www.masswerk.at/nowgobang/misc/MINAC-IRE-March-1957.pdf https://www.masswerk.at/nowgobang/misc/MINAC-IRE-March-1957....

masswerk 7y ago
Here's a photo (by Cory Heisterkamp) showing the logic networks from the Ed Thelen's website [1]: http://ed-thelen.org/comp-hist/images/Heistercamp-lgp.jpg http://ed-thelen.org/comp-hist/images/Heistercamp-lgp.jpg (The cards with the rest of the logic are behind and below the main network plane. Mind that this a Control Data model, so it's 1965 or later.) [1] http://ed-thelen.org/comp-hist/lgp-30.html http://ed-thelen.org/comp-hist/lgp-30.html
kragen 7y ago
This is awesome! Thank you! This should make the Boolean equations in the manual quite a bit easier to decipher. XOR isn't monotonic — you can't make X ⊕ Y with diode logic given just X and Y, the way you can make X ∧ Y and X ∨ Y. However, you can make it given X, Y, X̄, and Ȳ. I'm not sure if you can make it with X, Y, and just one of X̄ or Ȳ.
- masswerk 7y ago
  Regarding XOR: This is sloppy quoting of Frankel, who writes about the monotonic functions "And and (nonexclusive) Or" – so, yes, inclusive Or only. However, as described, both the normal and the inverted (negated) outputs of the flip-flops ("toggles") are fed into the network, so there's X and Y and negated X and negated Y available.
  - kragen 7y ago
    Right, and as I explained at https://news.ycombinator.com/item?id=20488446 https://news.ycombinator.com/item?id=20488446, if you have negated versions of all the literals available, you can make not just XOR but any arbitrary Boolean function as a sum of products (or a product of sums, CNF), just like a PLD does.
    - masswerk 7y ago
      Notably, you need XOR (single-bit add) for an ALU anyway… (So the somewhat weak exclusion of "exclusive" in Frankel's paper is a bit luxurious.)
      - kragen 7y ago
        "Luxurious"? I'm not sure what you intend to say. Do you perhaps mean "unnecessary" or "essential" or "very strong" or "very weak" or "well-thought-out"? As I read it, he's pointing out that since the diodes and resistors can't do things like XOR, because it's not monotonic, it's necessary for "[e]ach input variable" to be "presented in duplicate". Another example that is in some sense more fundamental than XOR is the MUX function b if a else c. If at some point b = 0 and c = 1, the output is the negation of A, which diodes and resistors alone cannot achieve.
        masswerk 7y ago
        "Luxurious" is a term from psychology, where it's used to describe "ornamental" behavior, which may be hinting at something deeper. ;-) In the particular case, I just found it interesting, since the duplicate outputs are already well established, before the text "withdraws" to monotonic functions (for which both inputs are used). A bit of an understatement. Edit: I think, "luxurious" as used this way is a great term, because it doesn't attempt to apply any classification. It's just pointing out that there's a somewhat independent process, which consumes energy.

masswerk 7y ago

Here's a photo (by Cory Heisterkamp) showing the logic networks from the Ed Thelen's website [1]: http://ed-thelen.org/comp-hist/images/Heistercamp-lgp.jpg http://ed-thelen.org/comp-hist/images/Heistercamp-lgp.jpg (The cards with the rest of the logic are behind and below the main network plane. Mind that this a Control Data model, so it's 1965 or later.) [1] http://ed-thelen.org/comp-hist/lgp-30.html http://ed-thelen.org/comp-hist/lgp-30.html

kragen 7y ago

This is awesome! Thank you! This should make the Boolean equations in the manual quite a bit easier to decipher. XOR isn't monotonic — you can't make X ⊕ Y with diode logic given just X and Y, the way you can make X ∧ Y and X ∨ Y. However, you can make it given X, Y, X̄, and Ȳ. I'm not sure if you can make it with X, Y, and just one of X̄ or Ȳ.

masswerk 7y ago
Regarding XOR: This is sloppy quoting of Frankel, who writes about the monotonic functions "And and (nonexclusive) Or" – so, yes, inclusive Or only. However, as described, both the normal and the inverted (negated) outputs of the flip-flops ("toggles") are fed into the network, so there's X and Y and negated X and negated Y available.
- kragen 7y ago
  Right, and as I explained at https://news.ycombinator.com/item?id=20488446 https://news.ycombinator.com/item?id=20488446, if you have negated versions of all the literals available, you can make not just XOR but any arbitrary Boolean function as a sum of products (or a product of sums, CNF), just like a PLD does.
  - masswerk 7y ago
    Notably, you need XOR (single-bit add) for an ALU anyway… (So the somewhat weak exclusion of "exclusive" in Frankel's paper is a bit luxurious.)
    - kragen 7y ago
      "Luxurious"? I'm not sure what you intend to say. Do you perhaps mean "unnecessary" or "essential" or "very strong" or "very weak" or "well-thought-out"? As I read it, he's pointing out that since the diodes and resistors can't do things like XOR, because it's not monotonic, it's necessary for "[e]ach input variable" to be "presented in duplicate". Another example that is in some sense more fundamental than XOR is the MUX function b if a else c. If at some point b = 0 and c = 1, the output is the negation of A, which diodes and resistors alone cannot achieve.
      - masswerk 7y ago
        "Luxurious" is a term from psychology, where it's used to describe "ornamental" behavior, which may be hinting at something deeper. ;-) In the particular case, I just found it interesting, since the duplicate outputs are already well established, before the text "withdraws" to monotonic functions (for which both inputs are used). A bit of an understatement. Edit: I think, "luxurious" as used this way is a great term, because it doesn't attempt to apply any classification. It's just pointing out that there's a somewhat independent process, which consumes energy.