Zahlenrepräsentation

Zahlenrepräsentation refers to the way numbers are stored and manipulated within a computer system. Computers fundamentally understand only binary digits, or bits, which can be either 0 or 1. Therefore, all numerical data must be converted into this binary format.

There are several common methods for representing numbers. Integers are typically represented using positional numeral systems, most commonly base-2 (binary). Positive integers can be directly converted from their decimal representation to binary. For negative integers, two common methods are two's complement and sign-magnitude. Two's complement is widely used because it simplifies arithmetic operations.

Floating-point numbers, which represent real numbers with fractional parts, are stored in a more complex format, often following the IEEE 754 standard. This standard divides the binary representation into three parts: a sign bit, an exponent, and a mantissa (or significand). This allows for a wide range of values, including very large and very small numbers, but introduces potential precision issues.

The choice of Zahlenrepräsentation impacts memory usage, computational efficiency, and the range and precision of numbers that can be represented. Understanding these representations is crucial for programming and for comprehending how computational limits and errors arise.