256-bit computing
There are currently no mainstream general-purpose processors built to operate on 256-bit integers or addresses, though a number of processors do operate on 256-bit data.

Representation
A 256-bit register can store 2256 different values. The range of integer values that can be stored in 256 bits depends on the integer representation used.

The maximum value of an unsigned 256-bit integer is 2256 − 1, written in decimal as 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935 or approximately as 1.1579 x 1077.

256-bit processors could be used for addressing directly up to 2256 bytes. Already 2128 (128-bit) would greatly exceed the total data stored on Earth as of 2010, which has been estimated to be around 1.2 zettabytes (over 270 bytes).

Hardware

CPUs feature SIMD instruction sets (Advanced Vector Extensions and the FMA instruction set etc.) where 256-bit vector registers are used to store several smaller numbers, such as eight 32-bit floating-point numbers, and a single instruction can operate on all these values in parallel. However, these processors do not operate on individual numbers that are 256 binary digits in length, only their registers have the size of 256-bits. Binary digits are found together in 128-bit collections.

Modern GPU chips move data across a 256-bit memory bus (or possibly a 512-bit bus with HBM3).

The Efficeon processor was Transmeta's second-generation 256-bit VLIW design which employed a software engine to convert code written for x86 processors to the native instruction set of the chip.

The DARPA funded Data-Intensive Architecture (DIVA) system incorporated processor-in-memory (PIM) 5-stage pipelined 256-bit datapath, complete with register file and ALU blocks in a "WideWord" processor in 2002.

Software
 256 bits is a common key size for symmetric ciphers in cryptography, such as Advanced Encryption Standard.
 Increasing the word size can accelerate multiple precision mathematical libraries. Applications include cryptography.
 Researchers at the University of Cambridge use a 256-bit capability pointer, which includes capability and addressing information, on their CHERI capability system.
 SHA-256 hash function.
 Smart contracts use 256- or 257-bit integers; 256-bit words for the Ethereum Virtual Machine. "We realize that a 257 bits byte is quite unusual, but for smart contracts it is ok to have at least 256 bits numbers. The leading VM for smart contracts, Ethereum VM, introduced this practice and other blockchain VMs followed."

See also
 Berkeley IRAM project
 Computational RAM

References

Data unit