Calculation Assistance Device

The Calculation assistance device (演算補助デバイス) is a device that Accelerator uses which allows his brain to connect to the Misaka Network and perform calculations for him to compensate for his lost verbal, motor, and calculation abilities. The latter allows him to use his esper powers. Created by Heaven Canceller himself, it takes the form of a Choker-style electrode (チョーカー型電極).

In Toaru Majutsu no Index it was used to balance Accelerator out with the other protagonists as well as the antagonists he confronts due to his incredible power. It also symbolizes Accelerator's ironic fate as the one who once had taken away the lives of 10,031 Sisters but now has his life being supported by the remaining 9,970 that lived.

Construction
After Accelerator's frontal lobe has been damaged after being shot by Amai Ao, it took away his verbal and calculation abilities. Moreover, it seemed to affect his motor skills as well as his ability to properly discern text and speech. After being told by Misaka 10032 that he can use the Misaka Network to do calculations, Heaven Canceller endeavored to construct a device to compensate for what Accelerator has lost. All of the important parts of the device was created by Heaven Canceller himself, manufacturing it through the use of machine tools.

Pre-modification
The device takes the appearance of a black rectangular box which contains most of the parts. There is a switch on the device that allows Accelerator to use three settings: off, normal, and esper mode, a little light on the box is indicating which setting Accelerator is using. Finally, a wire comes out of the box which splits in two. Each of its end has an electrode attached which is then stuck to the back of Accelerator's head. This makes the appearance of the device look similar to that of a portable music player.

The device makes use and transmits Accelerator's brainwaves to make a limited connection to the Misaka Network which is composed of the remaining 9,970 Sisters. To allow Accelerator to make use of the Misaka Network's calculations, the device acts as a transformer that can let both sides' brainwave wavelengths match. The device uses a unique battery that cannot be replaced, much to Accelerator's inconvenience. To recharge the device's battery the rectangular box can be removed from the choker and then attached to a dedicated power set. In the original construction, the device under normal settings can be used for 48 hours allowing for Accelerator to walk, talk, count, etc. after which it needs to be recharged. With regards to the esper mode setting of the device, due to the massive calculations that are needed to be carried out every instant when using his powers, the device's battery would be drained in only about 15 minutes, and even then, Accelerator believes that the power he temporarily recovered via the device isn't even half of what it was used to be. As a side effect, the device provokes hair growth to Accelerator.

Post-modification
After GROUP's technical team got their hands on the device, it allowed Accelerator to use the v mode setting up to 30 minutes. However, much to Accelerator's surprise, the technical team also tampered with the device, installing a safety device that allows for a higher-up to control it remotely as they see fit, seemingly allowing them to disable the device from switching to esper mode.

Despite Accelerator obtaining the plans and designs of the device from Heaven Canceller, he makes no apparent attempt to modify the device. Instead, he uses the information he gathered to modify his crutch, allowing Accelerator to block specific wavelengths after successfully analyzing it and using the equipment of the crutch. It works by producing an interference wavelength that can be reverse-engineered to specifically block that wavelength, to seemingly counteract the tampering done on the device by the higher-ups.

Weaknesses
As it uses electromagnetism/specific EM waves in order for the device to connect to the Misaka Network, it is also susceptible to signal interference as well. The device will not function properly if Accelerator use it while in a deep underground location, or if a jamming signal was used. The latter was compensated through the use of his modified crutch. Moreover, it is also susceptible to not working in places where electromagnetic waves can be scattered, such as the Third Resource Recycling Processing Facility, which when used may make him lose control of his powers. The device is susceptible to the Chaff Seed, and is implied to be with permanent magnets used on motors as well, though Accelerator didn't even allow it to come close to him.

It is implied that Electromasters like Misaka Worst can jam the signal with her electrical powers. There is an implication that any person that can interfere with the Misaka Network itself would render the device useless as well.