Zeroes and Ones

""The machine doesn't see Herc the way you or I see him. The machine sees Herc as a series of ones and zeroes...""

- Joel, Mystery Science Theater 3000, episode 410: Hercules Against the Moon Men

It is an oft-repeated maxim that anything that existed when you were born is mundane and old-hat, anything that was invented in the first third of your life is exciting and novel, anything invented in the second third of your life is scary and incomprehensible, and anything invented in the last third of your life is an abomination of science run amok and is bent on corrupting our children, destroying civilization and -- Hey! Get off my lawn you kids!

The personal computer more or less came about when TV writers were right in that middle third. Writers do not really understand neither computers, nor Internet, and -- despite the fact that a fair demographic can barely even imagine a world without them -- assume that no-one else does either. The results of this ignorance are ideas such as AI Is a Crapshoot or Everything Is Online. Another result is this trope.

With very few exceptions, whenever a computer plays a major role in a story, you can expect to be treated to some (ofttimes bizarre) exposition about how a computer works, just to make sure you understand what this magic affair of a typewriter tethered to a television really is.

Specifically, you are exceptionally likely to have a character helpfully explain that, "A computer sees everything as a series of zeroes and ones."

This can be meant to imply several things: a computer is not capable of abstract thought; a computer can deal only with certainties, not probabilities or shades of gray; a computer cannot lie; a computer must behave logically; a computer can be programmed by tapping in binary instructions morse-code-like by shorting across a circuit, among others. Most, if not all, of these things aren't actually true.

"A computer sees everything as a series of zeroes and ones." is true, but only in the same way as "a human sees everything as a matrix of hues and intensities" or "a dog is composed entirely of protons, neutrons, and electrons": it's technically correct, but not really meaningful in terms of interacting with the computer. The level at which a computer deals with "zeroes and ones" is the level of digital electronics, a level which is so far below the level at which you operate on the computer that it's actually comparatively difficult to deal with zeroes and ones directly. Even the most fundamental operations on a computer almost always deal with blocks of 8, 16, 32, or 64 of these zeroes and ones at a time. A simple computer circuit that adds two numbers and shows the result in two displays, will involve at least 7 basic integrated circuits and an insane amount of wiring. Modern circuitry is billions of times more complex, and the industry uses special hardware-description languages, such as VHDL, to automate the daunting task of designing such integrated circuits from scratch.

One common manifestation is that the writers treat binary as a language, when it's actually just a number format (also called base-2). A series of binary numbers has no implicit meaning unless you know exactly how its been encoded: what binary format is being used (is it 8 bit? big-endian? how are negative numbers handled?) and what the data is supposed to represent (ASCII text? color values? hit points?)

A computer manipulates data according to a set of rules. The way that data is represented has no meaningful impact on the "philosophy" of a computer beyond the difference between digital and analog -- which becomes completely academic if you toss enough bits at a problem.

Anime & Manga

 * Seen at end of Digimon Adventure:.
 * In Digimon Tamers, a lot of computer code is shown in binary but this is fact a subversion; what is shown is either ASCII (which is so ancient even Yamaki finds it insulting it is being used as a direct means of communication), or it was actually directly written in machine language (from a programmer that started in the 80's).

Films -- Animation

 * One of the better scenes in Battle for Terra is Mala talking Giddy into helping the Tarren forces by explaining the logic of his own orders to him.

Films -- Live-Action

 * Tron has the Bit, who acted as a sidekick to the hero and could only say "yes" or "no" (with a corresponding shapechange).
 * Rat in The Core has the memorable quote: "How many languages do you speak? I speak one: 10100. With that I could steal your money, your secrets, your sexual fantasies, your whole life. In any country, any time, any place I want. We multitask like you breathe. I couldn't think as slow as you if I tried." Possibly justified as an intentionally dumbed-down Badass Boast, but you don't want to start trying to justify The Core.

Literature

 * Neal Stephenson's Snow Crash has the similar mind-control system to "Whackets". A specifically crafted image can crash the brains of humans, but since the image is black and white and based on binary, it only works on computer programmers (as they have knowledge of binary ingrained into their brain).
 * Likewise, the short story Von Goon's Gambit tells the tale of a chess player who discovers a certain arrangement of chess pieces creates an alternating pattern of light and dark which constitutes a computer program that crashes the human mind. He becomes world champion by default (having driven all challengers mad) before he's lynched by a gang of respectable chess masters who've decided that what they really can't stand is a smart-ass.

Live-Action TV

 * Max Headroom: "Whackets" actually has a mind-control system that worked by flashing a series of zeroes and ones at the human viewer. Max himself proves exceptionally vulnerable, as he is inherently based on, you guessed it, zeroes and ones.
 * Red Dwarf: Spoofed by Kryten, who occasionally says proverbs in his "native" tongue.
 * Star Trek: The Next Generation did a first-season episode in which the computer-like Bynars race steals the Enterprise to save their homeworld. At the end, they claim that they didn't just ask because "You might have said no". Riker concludes that, as the Binars think like computers, it all comes down to zeroes and ones to them: yes vs. no, take the ship vs. don't take the ship. And if you think this metaphor doesn't make sense, that's because the plot of this episode wasn't very good. The title of said episode is "11001001", of course.
 * In the Stargate Atlantis episode "The Intruder", the computer monitor behind Hermiod displayed The Matrix-style scrolling columns... consisting entirely of the digits "0" and "1". You'd think the United States military would build something more sensible than that, given their supposed fondness of viewer-friendly interfaces.
 * It's worse than that, after staring at the scrolling numbers for a few seconds McKay immediately deduced that he was looking at a virus. He then went on to press a few buttons and translate the binary into Wraith, somehow confirming that the Wraith must have been the ones to write it.
 * Joe on News Radio once claimed to be able to read binary. In one episode, he reads Dave's letter on his computer, which had broken and was only showing things in binary format.
 * The Murder, She Wrote episode "A Virtual Murder" used the same concept as the TNG episode above, only instead of computerlike aliens, it's apparently regular human computer programmers who think like this. "One or zero", the murderer says at the end, "I swore a long time ago I'd never live in that grey world in between. It's got to be all, or nothing!"
 * An episode of Ghostwriter is a rare example of this trope not using the 0s and 1s metaphor. Instead, painfully outdated slang is used to describe how the computers work. A particularly egregious example in the episode can be seen here (given by Julia Styles).

Music

 * Referenced/spoofed in the Flight of the Conchords song "The Humans are Dead". It contains a "binary solo," which consists of Bret reciting sequences of ones and zeros out loud.
 * Rush: "One zero zero, one zero zero, one, SOS. One zero zero, one zero zero, one, in distress!"
 * In the song "Fibonacci Sequence" by the net-famous musician Dr. Steel. "All our gods and heroes / are only ones and zeroes."
 * "And all we ever were, just zeroes and ones" from "Zero-Sum" by Nine Inch Nails.
 * The trope name itself is the very last line in Rilo Kiley's "Science vs. Romance".

Newspaper Comics

 * This FoxTrot comic.

Tabletop Games

 * Mage: The Ascension had Virtual Adepts' trinary decks. They were described as the next step in the technomagic, and able to say, here I quote "In a stiff computer world of "yes" or "no", trinary decks are able to say "Well... maybe".".
 * This has a vague resemblance to the boolean logic concept called "null". True and false basically boil down to yes and no, while null pretty much means "not applicable" or "no value" or "unknown". This corresponds a bit to the Chinese zen concept of wú, a.k.a. mu.
 * It also resembles fuzzy logic, which pretty much corresponds to shades of gray.

Video Games
"Mia: The World [the name of the MMO this takes place in] is made of more than ones and zeros; there are more options than "yes" and "no"."
 * The videogame sequel to Tron, Tron 2.0 introduced Byte: although Jet initially thinks he's a Bit, Byte gets indignant and says that he's eight times smarter than any simple Bit. Ironically, this statement betrays the comprehension gap that leads to this trope: a byte is composed of eight bits, but has eight orders of magnitude greater capacity. If Byte played by the same rules as Bit, he'd be able to say 256 distinct things.
 * The first set of .hack games has one character expressing:

"Durandal: Do you remember the days when computers were simple, unreasoning things you could turn off and on like flashlights? [...] [Thoth] concerns himself with the states of off and on, good and evil..."
 * Alluded to in Marathon 2: Durandal, by an A.I. describing another A.I.:

Toys

 * Computer Engineer Barbie's laptop has "Barbie" spelled out in binary-encoded ASCII.

Web Comics

 * One of the notes frequently accompanying Schlock Mercenary comics mentioned that the creation of thinking A.I. was made possible by the evolution from the "binary digit" into the "trinary digit", allowing computers to think in terms of "yes", "no", and "maybe". (On a side note, it is also mentioned that the same logic that turned "binary digit" into "bit" also turned "trinary digit" into "tit", further discouraging females from persuing a career in programming.)
 * In Real Life, the trinary base unit is called a "trit". Possibly for that very reason. Base four and five units, however, would probably be "quits" and "pits".
 * This is a pretty egregious bit of Did Not Do the Research, especially considering that the artist worked for Novell.
 * The concept of possibility is handled not through adding a new logical value, but treating true/false as a continuum as opposed to a binary selection, allowing for values that fall between 0 and 1.
 * Trinary logic systems do exist, and are most notably used in databases. The third value, though, is not "maybe". but indeterminate, a.k.a. "I don't know."
 * Narbonic has this strip, in which Helen (normally a biologist) has been infected with computer geekdom.

Western Animation
"Annie Sullivan: Zero one, one zero, one zero, zero one. Helen Keller: [incomprehensible gibberish] Annie Sullivan: Zero one, one zero, one zero, zero one! Helen Keller: [garbled repetition of binary phrase] Annie Sullivan: Zero one! Zero one!"
 * Re Boot has an entire race of people, called Binomes, which are anthropomorphic zeroes and ones who can speak in binary. In one episode, a binome tells a joke in ones and zeroes, which, in this case, is actually a roundabout substitution cipher: if you translate the ones and zeroes into decimal numbers, then the decimal numbers into letters, it becomes "Take my wife, please!"
 * Similarly spoofed by Bender in Futurama.
 * "Hell Is Other Robots" has Bender giving a Robotology prayer in all zeroes and ones (though, oddly enough, it ends with "2").
 * "The Honking" has the sequence "0101100101" (357 written in binary with an unnecessary leading zero) appear on a wall, which Bender dismisses as "gibberish". He then immediately notices the sequence reflected in a mirror: "1010011010" ("666" written in binary) and freaks out.
 * And in "A Head in the Polls", he has a dream that turns into a nightmare when Bender thinks he saw a 2 (incidentally, there is one in the flash of 1s and 0s of his dream. Its visible just at the bottom as it ends).
 * In Bender's Big Score, it's revealed that the entire universe and time itself runs on zeroes and ones. Even money says it's a series of tubes, too.
 * The binary number on the door of Bender's apartment is the ASCII value of the dollar sign.
 * Prayers and ominous messages aside, Bender isn't actually fluent in binary, he just knows how to ask where the bathroom is.
 * In Code Lyoko, zeroes and ones are constantly filling up blue squares inside the Lyoko Towers, within the tunnels between the sectors, or over the surface of the Celestial Dome in Sector 5.
 * In one Family Guy episode a professor demonstrated the concept of binary language via a scene from The Miracle Worker done in zeroes and ones. Anne Sullivan tries to teach deaf & blind Helen Keller to say "water".

Real Life

 * Encoding things in Binary does create certain limitations that wouldn't otherwise exist. The common standard binary floating point format, for instance, cannot exactly encode "1/10" as 0.1 is actually a repeating numeral (the same way you cannot exactly write "1/3" in decimal: you have to either round up or round down or spend the rest of your life writing threes)
 * There other ways of encoding numbers into binary that can precisely handle fractions, and even irrational numbers, but calculations with these methods are much slower than calculations using floating point approximations.
 * Depending on how much precision you really need, you can get away with fixed-point arithmetic to do fractional operations. It's essentially dictating where 2^0 is. For instance, a decimal 1 could be in the 16th bit of a 32-bit number, meaning you have 16 more bits for fractions (which are negative powers of 2). The huge advantage is that not only do the addition, subtraction, and multiplication still work the same way, but you can essentially cheat division by multiplying by a fractional number. The Mind Screw is that you have to remember where 2^0 is defined, because unlike its name may indicate, the binary point can shift.
 * Related to the fact of binary computer chips, it is commonly stated that there is only "one" or "zero," depending upon the voltage flowing through them. However, if the voltage is turned off, it can't be either one OR zero, and is in what is called a "Mu State."
 * Also, high-impedance (effectively, a signal that is not there).
 * Or a "don't care" value.
 * Quantum computers are computers that don't use just zeros and ones. Lo and behold they're more (asymptotically) powerful than classical computers, or rather they might be if we can make them bigger than a few atoms in size.
 * If you really want to blow your mind, the fundamental unit of quantum computing is the qubit, which can be in a superposition of zero and one.
 * To give an idea of how strange this is, it has been proven that the fastest way for a computer to search an unsorted database is for it to search each individual record, taking n time to search n records. A quantum computer can search the same database of n items in squareroot(n) time.
 * To be a bit more clear, a quantum computer cannot do anything that a normal computer can't do, it can just do some things much faster. Quantum computers also aren't deterministic, which means that they have a (hopefully) small chance of actually returning a wrong answer. For these reasons practical implementations of quantum computers will almost certainly be paired with ordinary computers.
 * This is all based on the assumption that we get past the very real and sometimes very large physical problems of building such computers, not to mention making them economically feasible.
 * Well, seems like science has marched on.
 * The Soviets built a ternary computer, or a computer with 3 states. But in this case, it's not 0, 1, and 2, but rather -1, 0, and 1. There are some practical applications, but binary took off and the Soviets needed something compatible with the rest of the world.