This page contains information regarding Star Trek: Lower Decks, and thus may contain spoilers.
The Bynars were shorter in height than most humanoids and were genderless. They had lilac skin and enlarged skulls. Each Bynar had a patch of dark purple hair on both sides of their neck and asymmetrical ears. Their most definitive characteristic was that they were interconnected with a master computer on Bynaus. (TNG: "11001001") When a Bynar was born, a surgeon removed the child's parietal lobe and replaced it with a synaptic processor. (ENT: "Regeneration")
Bynars always worked and lived in pairs. There was a great degree of physical symmetry between each Bynar couple. For instance, each Bynar's pair of ears matched those of their partner, but were on the opposite sides of the head. Their typical clothing was also consistent in such a way. Because the Bynars were so interconnected with the master computer, their language and thought patterns became as close to binary code as possible. They could speak English, usually finishing each other's sentences. For example:
The Bynars' primary language was a high-frequency sound, unintelligible to Humans, though the Bynars used it when they spoke to each other. Every Bynar was equipped with a buffer, which they carried at their waist, to manage this rate of information transfer and had a small metallic component on one side of their head. Each of these mechanisms had a red light which blinked on and off when the Bynars were communicating between one another. Each of the Bynars had the component on the opposite side of the head from their partner, yet another aspect of their symmetry when grouped.
The development of the Bynar ability to constantly receive information but to store it, via their buffers, until it was necessary happened over a long period of time. (TNG: "11001001") By 2153, the Bynars had adopted their practice of replacing each of their newborns' parietal lobes with a synaptic processor. Doctor Phlox saw the procedure performed when he encountered the Bynars in the Beta Magellan system. In 2153, he remarked that the procedure had been "very impressive" and indirectly likened the Bynar way of life to, unknown at the time, a benign form of the Borg Collective. (ENT: "Regeneration")
In the 24th century, Starfleet employed Bynars to perform computer upgrades on its starships. A team of four Bynars was assigned to Starbase 74, under the supervision of Commander Quinteros. He appreciated the swiftness with which they carried out tasks.
The Bynars discovered that, although the extreme integration of technology into their society had tremendous benefits, it also had a few disadvantages. Due to the fact that an electromagnetic pulse from a supernova in their star system was due to knock out their planetary computer in 2364, the Bynars were left with only one choice: to temporarily deactivate the computer and transfer all the stored information, until after the pulse had passed.
The Bynars opted not to request that Starfleet assist in resolving the situation. This was because they thought in binary code, ones and zeroes, yes or no. Their need was so great they could not risk their appeal being rejected. Instead, since the USS Enterprise-D had the only mobile computer large enough to handle all the information from the planetary computer, the team of four Bynars stationed at Starbase 74 commandeered the vessel, during a computer refit. (TNG: "11001001")
Robert Lewin, who co-wrote "11001001" with Maurice Hurley, devised the concept of the Bynars while contemplating binary numbers in computers, thinking, "Maybe there are individuals who are binary, composed of binary cells and work as a pair." He later recalled, "Their strange way of finishing each other's thoughts, their whole unique attitude, the planet they came from, all that had to be worked out." (Starlog #191) As originally conceived, the Bynars were a race of creatures which did not talk but had another means of communicating amongst themselves. (Star Trek: The Next Generation Makeup FX Journal, p. 58)
The physical "look" of the Bynars also had to be given much thought. They were imagined, even from their inception, as small. (Star Trek: The Next Generation Makeup FX Journal, p. 58) They were scripted as "pale, frail people with translucent skin."  The Bynars were thereafter collaboratively designed by Michael Westmore and Andrew Probert. The coloration of their skin was influenced by Westmore. "At that time we had painted everything [alien] every color we could think, but we hadn't used purple yet," Westmore explained, "and they became my lavender alien race for the week." (Star Trek: The Magazine Volume 2, Issue 12, p. 26) Probert illustrated concept artwork for the Bynars, which he dated 1987, and later recollected, "I think I was asked to do the Bynars; I was certainly asked to do their equipment. The concept was that they were co-dependent. I think Michael suggested that their bodies would actually develop toward each other, which would give them a real asymmetrical look to their heads, which was something we hadn't seen before. He liked the ears that I put on them, but he did something different with the hair." (Star Trek: The Magazine Volume 2, Issue 12, pp. 48 & 49)
Even though the creative staff wanted the Bynars to be small, the use of children would have required bringing teachers in and raised concerns about the number of hours the children could work each day. (Star Trek: The Next Generation Makeup FX Journal, pp. 58-59) Like the Talosians from Star Trek: The Original Series episodes "The Cage" as well as "The Menagerie, Part I" and "The Menagerie, Part II", women were cast to play the supposedly unisex aliens. They were petite and very young. (Star Trek: Aliens & Artifacts, p. 108) One condition for casting the women who played Bynars was that they seem to have an appealing, childlike aura. (Star Trek: The Next Generation Makeup FX Journal, p. 59) The women were all dancers whose voice track was mechanically lowered in pitch. (Star Trek: The Next Generation Companion 3rd ed., p. 48)
The makeup for the Bynars consisted of a large appliance for the head, which was similar to a bald cap or a bathing cap. As well as covering the head, the prosthetic came over the bridge of the wearer's nose, cheekbones and the back of their neck. All the head appliances were cast from the same mold. Each piece consequently had to be trimmed to fit whichever actress it was meant for. Because of this, the join line to the skin had to be hidden, which is why the purple hair on the sides of their necks was added. (Star Trek: Aliens & Artifacts, pp. 108 & 110)
The small mechanisms on the sides of the Bynars' heads were illustrated by Andrew Probert, in his concept art for the species, and went on to be made by Michael Westmore's son, Michael Westmore, Jr.. (Star Trek: The Magazine Volume 2, Issue 12, pp. 48 & 26) The devices were essentially simple flashing lights. They were wired to a battery pack mounted on the actresses' waists and were controlled by the performers themselves. (Star Trek: Aliens & Artifacts, p. 108)
The Bynar speech was originally designed to be subtitled. (Star Trek: The Next Generation Companion 3rd ed., p. 48)
The depiction of the Bynars in "11001001" was considered to have been very successfully executed. Maurice Hurley commented, "[They] were just wonderful science fiction creations; that they dealt in this binary language and had their little buffers. [Michael] Westmore did some wonderful work on that." (Captains' Logs: The Unauthorized Complete Trek Voyages, p. 163) Westmore himself agreed the aliens "turned out very well," believing the light purplish color of Bynar skin "blended nicely with the neutral look of the costumes." (Star Trek: The Next Generation Makeup FX Journal, p. 59) Director Paul Lynch remarked, "[They] were great. Nobody seemed to know they were four very small girls we found. It was also interesting that they all talked in that kind of connective fashion." (Captains' Logs: The Unauthorized Complete Trek Voyages, p. 163) Likewise, Robert Lewin cited the way the Bynars talked "together at the same time" as a highlight of the episode. (Starlog #191) Patrick Stewart opined, "I was very fond of the Bynars – maybe it was their pretty dancers' bodies – and wished that we had met them more than once." (Star Trek: Aliens & Artifacts, p. 9) Jonathan Frakes wondered, "Why haven't they returned?" and went to say, "That was a very well conceived idea. They should have them as a regular on the ship to fix the engines or whatever the hell they do." (Captains' Logs: The Unauthorized Complete Trek Voyages, p. 163) While beginning work on TNG Season 6, Westmore offered, "I think we can do more with them if they ever return." (Star Trek: The Next Generation Makeup FX Journal, p. 59)
Though the Bynars are referenced in "Regeneration", the episode's final-draft script included no mention of them. This was due to the fact that the scene involving the dialogue about the Bynars (a scene with Phlox and Malcolm Reed in the armory aboard Enterprise NX-01), was written in after the episode was filmed. ("Regeneration" audio commentary, ENT Season 2 Blu-ray)
Outside of the canon of Star Trek, a team of Bynars (110 and 111) was assigned to the USS da Vinci in the Star Trek: Starfleet Corps of Engineers series. When 111 was killed, the remaining solo Bynar, 110, became known as Soloman, a regular in that series.
In the novel Quarantine, two Bynar children were on a shuttlecraft of the USS Gandhi, commanded by Lt. Thomas Riker and piloted by Ensign Shelzane, when the shuttle was hijacked by Maquis posing as DMZ refugees.