Speaks in Binary

Binary code: The base-2 number system. Occasionally known as the "language" of computers. However, it's not usually spoken. But when it is, it's this trope. It's usually used jokingly as robots "native" language.

However, "binary" is not a language: Raw binary data has no meaning without a structure describing what it is. The "binary language" could be anything from "English text encoded in ASCII" to "Ideas, each attributed to a 16-bit number".

Film

 * The old modem like chirping emitted by droids in Star Wars films is called "binary" in-universe. However, it's unknown whether it's binary as we know it and how is it encoded into sound.

Literature

 * Ashley, and all the other aliens, in Jasper Fforde's Nursery Crime series have binary as their native language. They also play binary Scrabble.

Live Action Television

 * In Star Trek the Next Generation, there is a race called the Binars, which speak to each other in binary.
 * Joe from News Radio claims to be able to read binary.
 * In Red Dwarf, Kryten uses binary as droidspeak on occasion. In "Terrorform" he gives a very long set of binary as an "old droid saying" about not standing and blathering when you're in mortal peril

Music

 * In the Flight of the Conchords song "The Humans Are Dead", there is a binary solo.

Newspaper Comics

 * Jason does this in a FoxTrot comic.

Tabletop Games

 * In Warhammer 40000, Tech Priests use binary as a secret language (although it's never been established if it's binary as we would know it). Justified by the fact that all of them are at least part machine.

Video Games

 * In Mass Effect 1, the final message from the rogue AI on the Luna Base is in binary. It translates into "HELP ME".
 * When from Kid Icarus Uprising, he speaks out loud in binary; it translates to "KILL".
 * Volt in Tales of Phantasia speaks almost entirely in binary, causing a misunderstanding between him and the heroes which leads to a fight, and later, a contract.

Web Comics

 * In The Order of the Stick, Elan considers a dilemma from a Law/Chaos viewpoint, and his Lawful Angel is a modron and speaks entirely in binary. It's not very helpful.
 * Reunited squirrel girls aka "Think Tank" in Sequential Art.

Western Animation

 * In Futurama, Bender says a prayer in binary. He ends with "2".
 * There's also the Time Code from Bender's Big Score, a long list of zeros and ones that is said like an incantation to send the speaker back in time.
 * In "Godfellas", the galaxy that may or may not be God signals Bender in binary. Bender mentions that he only knows enough binary to ask where the bathroom is (which contradicts the above, but hey, Rule of Funny).
 * In an episode of ReBoot where the Plucky Comic Relief told a joke in binary; the "binary joke" comes out to "Take my wife, please!" when translated into ASCII.