My wife @LibertyFarmNH gives the absolute best most amazing Christmas presents. This year was a bounty of nerdiness that would make weeaboo Smaug blush, but this one item was the piece we resistance!pic.twitter.com/pDelHcDxtU
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9/ But just to spell it out: adjust the sliders, rotate the crank. If we leave the sliders at 9 and add it again, the output now reads 30, and operation count is 3. Let's say that we didn't MEAN to add that last 9. We want to subtract it away.
10/ Pull the operating handle UP, revealing a white ring around its base, and rotate it 360°. The accumulator subtracts out the last 9, and the operation counter is decremented by 1. This is 95% of all there is to know!
11/ The key thing is that the operations counter counts acts of ADDITION. So subtracting removes one from the op counter. OK, a little odd, but it is what it is.
12/ Now, a small complication. Let's say that I want to multiple 123 by 2. This is easy. 123 x 2 = 123 + 123. I clear the outputs, set the sliders, crank it once, crank it twice. But what if I want to calculate 123 x 20?
13/ Clear the outputs, set the sliders, crank it once, crank again, crank it again ... crank if ... 20 times? That kind of sucks. And what if I want to add 123 ... say, 900 times? I've got to crank this 900 times?
14/ No, it turns out that there's a shortcut ! Remember that upper knurled ring, that we pulled up as part of the two step process to clear the outputs? Well, it has a SECOND function. When you pull it up you can ROTATE IT before you drop it back down again.
15/ It has 9 or so different settings. In the first / default / base setting, each turn of the crank adds the input to the accumulator 1 time. In the second setting, each turn of the crank adds the input to the accumulator 10^1 (=10) times.
16/ In the third setting, each turn of the crank adds the input to the accumulator 10^2 (= 100) times. And so forth.
17/ Notice that I do not say "adds 10x the input", but "adds the input 10 times". What's the difference? The operation counter. If I set sliders to 9 and turn the order-of-magnitude-ring to 3 (i.e. x 100), and then crank once, the operations counter now registers 100, not 1.
18/ The operations counter so far is an interesting curiousity, but we're going to use it when we do division. But before we do division we need to talk about subtraction. ...and I'll get to that later.
19/ EXCELLENT QUESTION ! Yes, there are a few reasons you might want to adjust the operations count. It turns out that there's a 2 position slider on the side for "regular op count increment" vs "REVERSED op count increment" ! https://twitter.com/DunsScottus/status/1210220268003741697 …
20/ I intentionally only read half of the instruction manual because I wanted to figure out the advanced stuff on my own, as a puzzle. Hopping ahead, the way division works is to push the dividend into the accumulator, then start subtracting out the divisor. e.g. 17 / 4
21/ So we clear the output, set 17 on the slider, crank it in, now the accumulator shows 17 and the opcount shows 1. We can clear the opcount by setting sliders to 0 and then pulling the stem to subtract and cranking once. Accumulator stays at 17, opcount is now 0 again.
21/ OK, we're ready to go. Set the sliders to 4, slide the opcount reversing switch to "reverse" (so now we count subtractions as operations and additions as negative operations). Crank. Accumulator 13, opcount 1. Crank. Acc 9, op 2. Crank. Acc 5, op 3. Crank. Acc 1, op 4.
22/ 17 / 4 = 4 (the opcount) remainder 1 (the accumulator).
23/ Let's divide 100 / 3. Clear the accumulator and opcount. Crank in 100. Pull handle to subtract, adjust slides, subtract out 0. Acc = 100, op = 0. Set sliders to 3. So...we're going to have to crank this 33 times, right? No. Remember the order-of-magnitude ring.
24/ First, adjust the opcount direction to reverse. Adjust the order-of-magnitude ring from 1 to 2 (so each crank is 10 ^ (2-1) = 10 operations). Crank. Accumulator = 70, op = 10 Crank. Acc = 40, op = 20 Crank. Acc = 10, op = 30 Adjust ring to 1 (10^(1-1) = 1)
25/ Crank. Acc = 7, op = 31 Crank. Acc = 4, op = 32 Crank. Acc = 1, op = 33 100 / 3 = 33 remainder 1.
26/ What happens if we weren't paying close attention and cranked one time too many? small brain: we've got the wrong answer medium brain: ...but we can fix it! Push the crank back to addition mode. Crank once We UNDO the extra subtraction, i.e. we UNDO both acc AND opcount
27/ galaxy brain: but what EXACTLY happened when we subtracted 3 from 1? Can we learn something interesting about math? Answer: YES, WE CAN ! But I'm going to work on fiction writing now. I'll talk about 10s complement math later. Also, how all this reminds me of Hoon.
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