Saturday Morning Post #82: Between Zero and One (Part 2)

In Part 2 of another short story from the 24 Exposures collection, our hero is dealing with a major internet outage circa 2001. In the first part, he learns that his high speed T-3 connection was accidentally backhoed up by the power company and won’t be fixed until the end of the week. Unable to wait that long, he decides to venture out in the world to find that most low-tech of replacements: A dial-up modem. Well, low-tech for him at the time, but the only tech for most people otherwise.

“Piece of shit.”

Tyler banged the dashboard with both hands, then tried the keys again. The starter whirred and chuddered, but nothing happened. It was sounding a little upset itself now, warbling instead of surging. Tyler pulled the keys out of the ignition and sat there, thinking. The battery wasn’t dead, he knew there was gas in the tank, the car had started last time he’d driven it, which was… thirteen, fourteen months ago. He vaguely remembered his father telling him something once about having to start up idle cars every so often, but that had never made any sense. It was a machine, it wasn’t doing anything while it was sitting there, inert. No stress, no wear. You could let a computer sit for years and it would start up fine next time you plugged it in.

Tyler got out of the car, slammed the door and gave it a kick. Well, who needed a car, anyway? There was a bus stop a block away, and that bus went in the general direction he needed to go. All he had to do was go check the schedule…

“Fuck!” he stomped one foot on the porch as he remembered. Check schedule, online, not possible. Again, the phone book was useless. It had some elaborate map of the transit system, with colored lines and arrows and little number tags, but it was like trying to read a circuit diagram for a nuclear bomb. No, not that. Even a nuke must have the same basic set-up as any other bomb. Explosive shit, power source, two wires, a switch and a bang. This was more like trying to trace the intricate pathways through the heart of the world’s biggest supercomputer, and Tyler was the lone little electron who had to go from point A to point B down the shortest possible path.

Well, screw it. The colored line for the bus that ran by his house seemed to get close to where he wanted to go. How long could he possibly have to wait, anyway? He kicked the phone book aside, started for the door, stopped. He was forgetting something, but what?

Ah. Change. Riding a bus always did involve clunky pocketfuls of change, anxiously counted out and recounted and clutched in the hand when the rolling leviathan finally pulled into view and hissed to a stop. He thought about it a moment, then remembered the mayonnaise jar on top of the fridge. It was way in the back corner, dusty and grimy. He hadn’t needed to take anything out of it nor had anything to put into it for a long time. He grabbed the lid, tried to twist it and it wouldn’t budge. Great. Just fantastic. He could understand, maybe, a car being slow to start after a while, but this was a goddamn jar lid, the simplest machine of them all, the one invented by some ancient Greek guy. It was a screw, how the hell could it malfunction? Tyler tried a dish towel, tried to get a wrench around the thing. This was ridiculous. Nothing. What, did some evil change imp come by and krazy glue the thing shut in the night?

Tyler heaved the jar into the kitchen sink, where it shattered, spewing coins all over the porcelain, half of them chittering down into a sinkhole in the drain. At least the stopper was sitting there, but he’d deal with all that later. He picked through the metal bits, pulling out all the quarters he could easily see, avoiding the shards of glass, grabbing up some dimes and nickels for good measure. He counted it out in his hand. Five bucks, twenty-three cents. Good enough for a round trip. He dumped it all in his pocket, where it felt cold and heavy through the lining against his thigh, then headed out the door again into the blinding bright sunlight of this late summer afternoon.

* * *

Forty-five minutes later, he was still standing at the bus stop, anxiously stepping out into the street whenever traffic cleared to peer into the distance, looking for any sign of his impending ride. Every time he thought he saw it, he’d jump back, start counting out his change, not sure exactly how much he needed, only to see that he’d been fooled by a school bus or a big truck. Forty-five goddamn minutes, that couldn’t be right. What good was that kind of transit system? They should have had a bus going by here every ten minutes.

He glanced at the tiny Hispanic woman in the pale blue dress who was standing nearby, full shopping bags hanging from each hand, two young children flittering about her. She just stared at the ground, stoic and patient. Tyler popped out into the street again, looked. Nothing on the horizon.

Another ten minutes went by, another half-dozen traffic checks, and Tyler was fuming all over again. The Hispanic woman had finally glanced his way, noticed him looking, nodded her head and said, “Late, huh?”

“Damn right,” Tyler replied, peering up the street again. This all seemed to be designed to waste his time. Why did this world outside move so slowly? Almost an hour of doing nothing. Tyler debated going back home, trying the car again. Maybe he could get one of his friends to come over and… okay, no, bad idea, since his friends were all over the country, all over the world. Did he know anyone locally? Well, maybe, yeah, but… Tyler rolled his eyes, huffed, realizing he only had a long list of email addresses, no phone numbers. Wasn’t that just peachy‑keen?

Then he noticed the woman picking up her bags, gathering her children close. The bus was coming, halle-fucking-lujah. He dug a fistful of change out of his pocket, turned to the woman. “How much?” he asked.

“Yes,” she smiled and nodded back at him.

“No, I mean, how much is the bus?” he repeated, demonstrating with the change. Before she could answer, the bus steamed right past them. Tyler turned his head, saw that it was empty, a “Not in Service” sign winking at them on its flank.

“Motherfucker!” he screamed, turning like a sunflower to follow the departing traitor, change tumbling from his hand into the gutter. The woman pulled her children close, looking away as Tyler got down and started picking the stuff up. Naturally, it was now all wet and gunky. Oh joy.

Twenty minutes later, another bus finally arrived and pulled up to the stop. As Tyler waited for the woman and her kids to climb on, he looked up the street. There were two more buses on the way, right behind it, pulling toward the curb.

“People suck,” he said to himself as he climbed the stairs, asked the driver how much and counted the right amount out, dumping it into the fare box, then moving about two feet before realizing that this bus was SRO. But it was too late to change his mind. The doors shut and the bus lurched away.

Okay, so he’d have to stand here with all this sardinated humanity. At least he was on his way. Finally.

* * *

“End of the line, everybody off,” the driver announced. People started spewing out both doors, pushing past Tyler, who stood there, perplexed. They were at the subway station, a mile from where he’d gotten on, but that’s not what the map in the phonebook had said. He could have walked to where he wanted to go already, and halfway back home.

He turned to ask the driver how to get where he was going, but she was already gone, as were most of the passengers. He got off and found himself standing in some sort of home for wayward transit. There were eight buses parked in various spots around a semi-circle, people milling back and forth between them and the over-sized, overly festive entrance to the subway station. Now what? He knew the subway didn’t go where he wanted. What were they thinking when they built that damn thing? It was great if you wanted to go downtown, but who the hell ever wanted to go there? And a subway, in LA, which had taken decades to get off the ground and which was only a pale, lame replacement for the transit system the city had had decades ago. A subway in the land of sunshine and earthquakes. Brilliant.

He walked the semi-circle, looking at bus numbers, finally finding the familiar one. The driver was standing on the front bumper, washing the windows.

“Which way does this bus go?” he asked.

Without looking at him, the driver drawled, “East.”

“Thanks,” Tyler replied, heading for the steps.

“Not leaving for thirty minutes, though,” the driver continued, concentrating on some invisible flyspeck.

“What?” Tyler gawked, stepping back. “Is there an earlier bus?”

“That one,” the driver nodded as another bus pulled past them, lumbered for the driveway.

“Fuck!” Tyler shouted, running for the bus, pounding on the side. Amazingly, it stopped and he got on, had to count out the change all over again. At least this one was half-empty. He went to a seat in the back, flopped himself into it and it was a good half mile before he realized they were going the wrong way, back to where he’d started. He grabbed the bell cord, pulled it frantically, heaved himself to the center doors.

When the bus finally stopped, he was right back where he’d started, full circle. Just to add a proper twist to the finger the gods were giving him, another bus going the other way, destination sign announcing exactly where Tyler wanted to go, fumed past and vanished into the distance.

“Everything sucks,” Tyler said to himself as he stared at the bus, just wanting to cry.

* * *

Saturday Morning Post #81: Between Zero and One (Part 1)

In another short story from the 24 Exposures collection, I flash back to my own life around the time I wrote this, in 2000 or 2001. This was pretty much the state of the internet at the time, and I was working from home as a graphic designer, little suspecting that I would be doing something very similar 20 years later but enjoying it a lot more. Like the lead character, I’m also very big on doing my own hardware and software upgrades, and get easily frustrated when tech fails.

Unable to locate host.

“Piece of shit.” Tyler banged his mouse against the desk in his usual litany of frustration, clicked reload. He waited two seconds, the limit of his patience, clicked reload again. Nothing, and then the error box of death popped up again with its annoying reminder noise. Unable to locate host.

“My ass,” Tyler shouted at his monitor. Still, he couldn’t help but always titter at that error message. It sounded like something an addled priest would say during Mass. Oops, I seem to have misplaced Jesus today… Of course, it had been a long, long time since Tyler had set foot in a church. Or anywhere, for that matter.

He let go of the mouse, went to the keyboard and hit control “R,” holding the keys down as the screen flickered. “Reload this,” he muttered, waiting.

Infinite seconds of nothing, annoying sound, error message the same again.

“Fuck.” Tyler spat. Okay, fine, maybe somebody had hacked the site — although he would hope that a major bank, his bank, was fairly hack-proof. No, it was some transitory problem, something stupid and mechanical, a broken switch or system traffic. Everything would be back up soon. Well, what the hell, in the meantime he could check out his favorite group look at some porn.

He went to his favorites, the folder named “Babes,” scrolled down to “Lusty Busty Beauties” and clicked. This was always good for a few minutes of amusement, any time of day.

Why was everything taking so long? He wasn’t connected by modem. That was so 1998. He was jacked in direct on a T-3 line, forty-five million bits a second. The first naked babe should have popped up on his screen instantly, if not faster.

UNABLE TO LOCATE HOST.

Tyler stared at the screen, frustration mounting. What was going on here? The problem must be on his end. He exited his browser, checked to make sure the operating system didn’t still think it was running (he was going to have to email a nasty note to the browser people over that recurring problem) then ran the program again, waiting.

The error came back, hovering over the empty gray screen of an unconnected browser. “Oh, fuck you,” Tyler grunted. He exited the browser, then rebooted the system. Billions of dollars spent on developing and marketing software and operating systems every year, and they still couldn’t get them right.

While his computer died and came back to life, he padded out to the kitchen, stepping around knee-high stacks of magazines and personal papers, grabbed a cup of coffee from the pot, took a sip. He glanced at the clock. It was four-thirty. Good, so it was just past noon in England and only about ten‑thirty tomorrow night in Sydney. He felt like chatting with some of his friends, maybe he’d do that when he was done with the banking.

He wandered back to the second bedroom he used as an office, where his computer was just finishing up the ever so long process of restarting. He sat down, ready to go back online when another error message popped up. “Unable to establish connection.”

He let out a frustrated shriek, then reminded himself of rule number one in the computer business — check for low density, high impedance connections. To the non-geek world, that was better known as a pulled-out plug. Sure, that must be it, simplest thing in the world to fix. He got down on his hands and knees, stuck his head far under the desk and peered around the back of his computer case as best he could.

He banged his head on the desk when he started to emerge for the flashlight. What idiot had ever decided that all the connections should be on the back of the computer, anyway? Even with the radio linked keyboard, mouse, printer and webcam, there was still an octopus of cords back there. Tyler grabbed the flashlight and turned it on. Then, he stared at the thing, which refused to illuminate. He flung it across the room, then turned on the overhead light, got back down under the desk and moved the computer to the side, tilting it and squinting.

Everything was plugged in where it was supposed to be. The thick blue wire was firmly in its socket. He jiggled it just to make sure. Yep. Connected. He traced the wire to the wall, where, likewise, it was firmly connected. He unplugged it, put it back in place until it clicked, just to make sure.

This was disconcerting. He heaved himself back into his chair, stared at the screen, then started checking out the settings for his network card. Nothing had changed, everything was correct. He knew these settings by heart, and they were fine. He tried connecting again. Nothing.

If Tyler designed operating systems, these error messages would be the first thing to go, replaced by a graphic of a hand giving the finger. That’s all they were anyway, the computer’s way of saying, “I know there’s a problem, but I’m not going to tell you what, exactly, it is. Nyah, nyah, human.” Was it too much to ask a three thousand dollar piece of plastic and metal with a three hundred dollar operating system to be a little more forthcoming when it failed? Shit, doctors wouldn’t make very much money if they worked that way. “Sorry, Mr. Smith, you’re dying. We don’t know what of, and we can’t stop it, but you’re done for.”

“Motherfucker…” Tyler shouted, banging the desk. He sat there, nostrils flaring for a moment, then shut down the computer and grabbed the screwdriver. “Prep the patient,” he said to himself. “We’re going in.”

* * *

Several hours, five cups of coffee, many reboots and an assload of frustration later, Tyler threw down his screwdriver and fell into a kitchen chair, wanting to cry. He’d taken the network card in and out five times, trying it in different slots, playing with the switches on it, flipping back and forth through the manual, which was about as informative as those error messages. Nothing worked. Every time he tried, every time that he knew this would be the time, it was the same thing. Nothing. Nada. Zip. Zero.

The sun had come up and he could hear neighbor’s cars starting, people heading off for their day. The poor, deluded fools, hurrying off to the rat race which would always begin with some hellishly slow commute, racing the clock and always losing, to go sit in someone else’s place and do someone else’s business and give up every bit of freedom. Tyler had gotten out of that game a long time ago, discovering the joys of telecommuting and Internet consulting, and he didn’t miss any of it.

Except, right now, he could be working and he wasn’t, for reasons he couldn’t fathom. He put the computer back in place, turned it back on, knowing it would be no different this time, and sat there, fuming. He grabbed his Rolodex, flipped through it and found the card for his service provider. He’d listed their customer service hours from eight a.m. to five p.m..

Great, so he’d have to wait two and a half hours? He was about to start cursing all over again when he remembered that the company’s offices were in New Jersey. Maybe that meant eastern time. Maybe he was in luck…

He dialed and waited, listening to the Muzak and the “Someone will be with you shortly” message. He put the phone on speaker and popped up his graphics program, idly flipping through the many photos of women he’d collected, scantily clad and less so, a gallery of objects that were all his any time he wanted them.

He was staring at the unblemished, golden round ass of a girl identified as Tracy (although he’d also run across her as Donna, Eileen and Kitten) when a voice intruded on the speaker. Tyler snatched up the phone. “Yeah, something’s wrong with my connection…” he said, voice cracking and gravelly this early in the morning.

“Let me check that for you, sir,” the chipper voice on the other end said. Tyler hated being called sir on the phone. He was only twenty-six, although he always sounded older. After the usual interminable business of giving his information and proving who he was, the Muzak was back and he waited again. He looked at the girl on the screen, wondered if the girl on the phone looked anything like her. Probably not. But he could pretend.

It seemed like hours but was really only two songs later that someone came back on the phone, but it wasn’t the girl. It was a man, who identified himself as a supervisor. Tyler’s heart fell. Now what? He’d paid his bill. At least, his bank did, automatically, every month. Unless they’d fucked that up.

“Mr. Allen, sorry to inconvenience you, but we’ve had a problem in your area,” the supervisor explained, trying to sound jovial.

“What kind of problem?” Tyler demanded.

“A construction crew — the electric company, actually — well, they cut right through our main fiber-optic line with a backhoe. Our entire system is down on the west coast because of it, but we are taking steps to get it back up.”

“They backhoed your backbone?”

The man laughed. “You could put it that way.”

“So, it’s not my computer?”

“No, no. It’s us. I’m real sorry about this. We will be offering a free month’s service to all of our customers, once things are resolved.”

“How long’s it going to be out, then, a couple of hours?”

“Well, Mr. Allen, I’m afraid not. It’s going to take a little bit longer than — “

“How long?”

“At least until Friday,” the supervisor said quietly, his jovial tone gone.

“Friday!” Tyler screamed. “Fucking Friday?”

“At the earliest, yes.”

“What the hell am I supposed to do until then?”

There was a pause on the other end, then the supervisor went on. “We are doing everything we can to restore your service as quickly as possible, Mr. Allen. We did explain all of this as soon as we knew about it, we sent an email to all of our customers.”

“You sent an email?”

“Yes, it explains everything.”

“An email?”

“Yes, did you get it?”

Tyler wanted to bite the phone in half. As it was, his left hand was practically splintering the plastic. He stood, breathing heavily. “Of course I didn’t fucking get it, you goddamned asshole. How the fuck can I get a fucking email if your fucking system is blown all to fuck for fuck’s sake?”

“Mr. Allen, there’s really no need for such language.”

“Fuck… you!” he screamed, then he slammed the phone down. Friday. Friday at the earliest. No, that couldn’t be. It was a bad dream, that’s what it was. He had work to do, clients to satisfy, people to chat with, things to… look up. Friday may have been their answer, but Friday was no good. To hell with Friday, he needed to be connected right now.

He was about to go online to look up other service providers when he realized that was a stupid idea, then went all around the house looking for the phone book. He finally found it under the bed and, even though the “Use Until” date on the cover was over a year ago, he flipped through it, found Internet Service Providers and started calling… and then realized that, while it may have been well into that supervisor’s work day, things still hadn’t really started out here and this was the local phone book.

Jesus, was that an archaic idea. Just local numbers? When would the phone company figure out that business had gone global? If he could look it up online, he’d find a company on the east coast that was ready to deal in five minutes.

But if he could look it up online…

Tyler slammed the phone book, stared at the clock, then stomped out to the kitchen. He’d have to wait two or three hours. Two or three hours, or wait until Friday. At the earliest.

Life sucked.

* * *

“Sure, we can get you T-3 service, you say you have all the hardware set up?”

“Yes,” Tyler said hopefully.

“And I’ve checked your location, we do service that area.”

“Great, great,” Tyler said. “So, how soon can you do it?”

“Let me check…” the woman paused, consulting something. “I can have a technician out there in… three weeks.”

“But I don’t need a technician, everything is set up, just turn it on.”

“That would be our self-service option — “

“Yeah, yeah, self-service, whatever. How long does that take?”

“We can have your service activated by… a week from Thursday. And right now, we have a special promotion — ”

“A week from fucking Thursday?” Tyler said.

“Y-yes. And our promotion — ”

“No sooner?”

“No, sir, I’m sorry.”

“And don’t call me sir.”

“All right. It’s a very good promotion  — ”

“Ram your fucking promotion up your ass, bitch.”

And he slammed down the phone for the seventh or eighth time that morning. He’d lost count. What was the problem with people? In theory, it would take all of five seconds to reroute his hook-up.

He had a DNS, his computer was a server, just send someone out to swap the wiring from the old company to the new one’s cables, change a little designation in a database somewhere, let it propagate, and bang, he’d be back in business.

The whole point of humans creating the internet in the first place was so that the entire system of military and university computers would stay connected, and no information would be lost in the case of all-out nuclear war.

Somebody had explained it once as the difference between good Christmas tree lights and shitting ones. If you bought shitty lights, where everything was wired in series, if one bulb burned out, the whole string went dark. But if you bought the good lights, where everything was wired in parallel, if one bulb burned out, none of the others would even notice.

In theory. The weak link was the human link, as in it would take some poor lazy asshole to get up out of a chair and go do something, and that was what took all the time, all the waste, all the frustration. That was the real reason computers sucked when they failed. They were designed by humans. Machines should have been superior to their creators, but they were not.

Of course, if that was the case, the human condition really did not bode well for the creative abilities of god.

It was noon by the time he finished with the last company, heard the same refrain. The earliest anyone could hook him up was a week and a day. The real world operated at a snail’s pace. He hung up with a quiet, “No, thank you.” He’d long since used up all the good profanity he knew, getting pretty creative around the twentieth call, pretty resigned by the thirtieth.

Of course, there was always the annoying fallback of using a dial-up service, even if it did mean switching temporarily to a regular modem. He went to the linen closet, opened it and surveyed the graveyard of abandoned peripherals. There were CD‑ROMs, floppy drives, old keyboards, two printers, a trackball, half a dozen joysticks, an ancient black and white webcam, a newer but just as outdated color one, and a stack of cards with uses that Tyler had practically forgotten. He pulled down the cards, flipped through the stack looking for that familiar UART chip.

Nope, nope, not that one, no, no… none of them were modems. None of them. That was unbelievable. He’d been through a dozen modems in the last five years, he had to have one sitting around.

Then he remembered. The day he’d gotten his T-3, he’d burned all the modems, actually put them in a metal bucket, doused them with lighter fluid and gleefully torched them. Sure, it had set off the smoke alarm in the living room, but it had been worth it. Ancient history, consigned to the fate it deserved.

In retrospect, it had been a really bad idea. But it was the thought that counted, and Tyler knew what he had to do now. Go out, buy a modem, and deal with it until Friday. At the earliest.

He started for the door, then realized he was wearing his robe and pajamas. Oops. Change first, then go out. He went to the bedroom, dug through the mound of laundry, found some clothes that didn’t smell too bad and changed. Okay, that was done with, now… wallet and keys, that was it. Wallet and keys, where were they? He hunted around the house for a good fifteen minutes before he found them, dusty and forgotten under a stack of magazines.

He also found his watch, which was actually still working. He looked at the date on it. September 10th. That sounded familiar. It took him a minute to remember, then he realized it had been just over a year since he’d last gone out this door. He hadn’t had to. He did all his business online, got paid by his clients through direct deposit, ordered everything from the Internet, even his groceries, had it all delivered.

He never went out to the movies but consumed a steady stream of DVDs by mail rental, ordered his stamps, his books and his CDs, got his news of the world, had all his friends, online. He knew people all over the world, chatted with them incessantly. He had sex with a lot of them, in the safest way possible, sometimes with the webcam, sometimes just with words.

He’d probably gotten off a lot of middle-aged businessmen who pretended to be teenage girls that way, but as long as Tyler didn’t know, he didn’t care. And if that method failed, there was always Kitten or Donna or Eileen, or whoever they really were, just an assortment of glowing dots writhing all over his great, big twenty-one inch monitor, beckoning him in the dark.

It was like somebody had cut both his legs off with that random backhoe. He wondered if the company had been lying to him. Was it really the power company? Blaming the power company in California was like blaming Palestinians in the Knesset. Was his service provider lying to cover up an inevitable act of human negligence and laziness?

That still didn’t change the length of time he’d have to wait, and he couldn’t wait. He put on his watch, pocketed his wallet and keys, went to the front door and grabbed the knob. He took a deep breath, then pulled the door open and stepped outside.

* * *

Being a basic bit

Zeroes and Ones are the building blocks of what’s known as binary, and the juice that our digital world runs on. Another way to think of it is this. In our so-called Base 10 world, we deal with ten digits, and depending upon what you’re counting, you can either go from 0 to 9 (things) or 1 to (1)0 (dates, place order). Since 9 is the highest digit, when any column hits it, the 9 next rolls back to 0 and the digit to its left increments up, initially from 1.

So after the number 9, we get 10. After 19, we get 20, after 99, it’s 100, and so on. Also note that 100 happens to be 10 x 10, 1,000 is 10 x 100, 10,000 is 100 x 100, etc. This will be important in a moment.

In the binary world, things roll over faster. In fact, the only digits you have are 0 and 1, so counting works like this: start with 0, then 1. But 1 is as high as we can go, so after 1 comes 10, which, in binary, represents 2.

That might seem strange, but here’s the logic behind it, going back to decimal 10. What is 10, anyway? Well, it’s the number that comes after we’ve run out of digits. Since we’re used to base 10, it doesn’t require any explanation to see that 10 always comes after 9. At least in base 10. I’ll get to that in a moment, but first there’s a very important concept to introduce, and that’s called “powers.”

The powers that be

No, I’m not talking Austin Powers. Rather, raising a number to a power just means multiplying the number by itself that many times. In its basic form, you’ll often see Xn. That’s what this means. It’s just a more efficient way of writing things out:

            2 x 2 = 22 = 4

            3 x 3 x 3 = 33 = 3 x 9 = 27

            10 x 10 x 10 x 10 x 10 = 105 = 100 x 100 x 10 = 10,000 x 10 = 100,000

Here’s an interesting thing about powers of 10, though. The end result will always have exactly as many zeros as the exponent, or power that you raised 10 to. 109. Simple: 1,000,000,000. If it’s 102, 100, and so on.

And the two fun sort of exceptions that aren’t exceptions to keep in mind:

            X x 0 x N = N, aka X0 = 1

            X x 1 = X1 = X.

101 is 10 with 1 zero, or 10; 100 is 10 with no zeroes, or 1.

In other words, any number to the power of zero equals 1, and any number to the power of 1 equals itself. And there you go, that’s all you need except for this: When it comes to determining what the power is, we count “backwards” from right to left. The last digit before the decimal takes the 0 power, next to the left is 1, next over from that is 2, and so on.

Everything in its place

Since places correspond to powers, in Base 10 we would call the digits, right to left, the ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, and so on places. In binary, you’d have the ones, twos, fours, eights, sixteens, thirty-twos, etc.

Makes sense? Then let’s look at a four-digit number in binary: 1776.

But here’s an interesting trick: in computer logic, it often becomes much easier for the circuits to literally read in the digits backwards in order to do these steps upwards in the proper order. This saves the step of having to figure out how long a string is before assigning the proper power to the most significant digit, which is the last one on the left.

So, to calculate, we’ll count it from right to left, which will make it easier to follow what’s happening. Let’s go with 6771 for ease of use. The 6 is in the zero position, so it represents 6 x 100, in which case this is 6 x 1, meaning just plain old 6.

Next, a 7 times 101, which is just 10, so this spot is worth 70 and we’re up to 76.

Next, 7 times 102, which is 100 times 7. Add that to the rest, it’s now 776.

Finally, a 1 in the spot multiplied by 103, which is 10 x 10 x 10, which is 10 x 100, so… 1,000. Slap that on the rest, and there you go: 1776.

This works exactly the same way in any other base. So let’s look at a typical binary number: 1011 1110. As humans, we could deal with doing the whole thing backwards, but again, let’s make it easy for the machine, feed it in right to left, and watch the sequence in action:

Digit (D) 0    1    1    1    1    1    0    1
Power (p) 0    1    2    3    4    5    6    7
2^p       1    2    4    8    16   32   64   128
2^p x D   0    2    4    8    16   32   0    128
SUM       0    2    6    14   30   62   62   190

Or in base three or trinary, let’s look at 21221121, entered again in reverse:

Digit (D) 1    2    1    1    2    2    1    2
Power (p) 0    1    2    3    4    5    6    7
3^p       1    3    9    27   81   243  729  2187
3^p x D   1    6    9    27   162  486  729  4374
SUM       1    7    16   43   205  691  1420 5794

Now, let’s take a look at an interesting property in Base 10 and see if it translates over.

Dressed to the nines

In Base 10, any number divisible by nine also has all of its digits add up to nine. You can easily see this with the first few pairs of two-digit multiples of nine: 18, 27, 36, 45, 54, and so on. The tens digit goes up by one while the ones digit goes down by one, and that makes perfect sense. Why? Because when you add nine, what you’re really doing is the same as adding 10 and then taking away one.

It doesn’t matter how big the number is. If you can add the digits up to nine, then you can say it’s divisible by nine. To just pull a number out of thin air, I guarantee that 83,764,251 is evenly divisible by nine. I could also put any number of nines anywhere in that number and it would still be divisible, or put the digits in any order. And if you have a number that has all of the digits from 0 to 9 in any order, then it’s divisible by 9.

So does this property hold for other bases? What about Base 8? In that case, we should expect seven to be the magic number. I’ll spare you the torturing of Excel I did to run a  test, but the answer is: Yes. If a number is divisible by seven in Base 8, then its digits add up to seven. Here’s the list from the Base 8 equivalent of 1 to 99 (which is 1 to 77): 7, 16, 25, 34, 43, 52, 61, 70. Now none of those numbers in Base 10 is divisible by seven, but in Base 8 they are. Here’s how and why it works.

When you divide a number in Base 10 by 9, you start on the left, figure out how many times 9 goes into that whole number, carry the remainder to the next digit, and repeat the process. So to divide 27 by 9, you start by dividing 20 by 9. This gives you 2 times 9 = 18. Subtract 18 from 20, you get 2. Carry that over to the next place, which is 7, add 2 and 7, you get 9, which is divisible by 9. Add the 2 from the first result to 1, and your answer is 3.

Did you notice anything interesting there? It’s that you happened to wind up with the number in the Base digit twice. Two times 9, with the remainder of 2 adding to the other digit, and what was the other thing we noticed? That’s right. The sum of the digits is 9, so what’s left when you divide the ten’s digit by 9 has to add to the one’s digit to total 9.

This is true in any other base. Let’s look at our Base 8 example of 34. We can’t cheat by converting to Base 10, so the 3 tells us that 7 goes into the number three times. But since 3 times 7 is 3 less than 3 times 8, that’s our remainder. Add that to the 4 to get 7, and boom, done. In Base 8 34/7 = 3+1 = 4. Convert the Base 8 to Base 10 to get 28, and voila… 4 times 7 is 28. The answer is the same either way when you reduce it to a single digit.

A spot check bears this out with other bases, so it would seem to be a rule (though I’m not sure how to write the formula) that for any Base, B, and any number evenly divisible by B-1, the digits of that number will add up to B-1.

That’s the funny thing about whole numbers and integers. They have periodicity. What they do is predictable. Multiples of any integer will appear at regular intervals without jumping around no matter how far towards any particular ∞ you go. Irrational numbers and primes, not so much. But it’s good to know that the basis of digital computing is so reliable and regular. In fact, here’s a funny thing about binary: Every single number in binary is evenly divisible by 1 because all of the digits of every single number in it adds up to a number divisible by… 1. And a Base 1 numbering system is impossible, because the largest possible number in it is 0. It also breaks the whole Base rule above, because nothing can be divided by 0. Base 1 is the Black Hole of the numbering system. The rest should be pretty transparent.