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The storage of real numbers in a computer involves representing them in a binary format because computers operate on binary digits (bits). There are several methods for representing real numbers, each with its advantages and limitations. The two most common methods are fixed-point representation and floating-point representation.

Fixed-Point Representation:

Fixed-point representation is a method where a specific number of binary digits (bits) are allocated for the integer and fractional parts of a real number.
The position of the binary point (analogous to the decimal point in the decimal system) is fixed.
For example, in a 16-bit fixed-point representation with 8 bits for the integer part and 8 bits for the fractional part, the binary point is assumed to be between the 8th and 9th bits.
Fixed-point representation is simple but has limited precision, and the range is fixed by the number of allocated bits.
Floating-Point Representation:

Floating-point representation is more versatile and widely used in modern computing.
It follows the IEEE 754 standard for binary floating-point arithmetic.
A floating-point number is represented as a sign bit, an exponent, and a fraction (mantissa).
The sign bit indicates the sign of the number (positive or negative).
The exponent represents the order of magnitude, allowing representation of a wide range of values.
The fraction (mantissa) represents the significant digits of the number.
The IEEE 754 standard defines single precision (32 bits) and double precision (64 bits) formats.
Example of a 32-bit single-precision floating-point format:

mathematica
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S Exponent Mantissa
1 8 bits 23 bits
Example of a 64-bit double-precision floating-point format:

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S Exponent Mantissa
1 11 bits 52 bits
Floating-point representation provides a larger dynamic range and precision compared to fixed-point representation but comes with some trade-offs, including potential rounding errors due to limited precision.

It's important to note that floating-point arithmetic may not always be exact, leading to issues such as rounding errors, especially when dealing with irrational numbers or numbers with many decimal places. Developers need to be aware of these considerations when working with real numbers in computer programs.