E.5 SUMMARY

Binary numbers provide a compact and consistent means of representing any numerical value using only two symbols, 0 and 1. Because binary arithmetic aligns directly with the operation of digital logic circuits, it forms the foundation of all digital computation, storage, and communication. The simplicity of binary representation allows digital systems to perform reliable arithmetic, logic, and control operations using only combinations of logic gates.

Arithmetic in binary follows straightforward rules: addition and multiplication correspond directly to the logical XOR and AND operations, respectively. These relationships underpin the implementation of adders, multipliers, and error-control mechanisms such as parity generation, block coding, and cyclic redundancy checks.

Beyond representing numbers, binary patterns can also encode symbols and characters. The American Standard Code for Information Interchange (ASCII) maps seven-bit binary combinations to 128 printable and control characters, forming the original basis for text representation in digital systems. For global communication, Unicode and ISO 10646 extend this concept, using 16-bit (and higher) encodings to represent more than 65,000 characters drawn from virtually all written languages, along with mathematical, scientific, and technical symbols.

Taken together, these ideas demonstrate the versatility of binary representation. Whether expressing quantities, logic states, or language itself, binary encoding provides the universal framework that underlies modern computing and digital communications—from the lowest-level circuit operation to the highest-level information exchange.