IEEE-754 Double Precision Converter

TYPE: Memory_Analyzer|ARCH: 64-bit

> Enter a decimal value (e.g., 0.1)

> Memory_Dump_64bit

Theory of Operation

The IEEE 754 standard represents real numbers in memory using a normalized form structured in the following equation:

(-1)^S × (1 + M) × 2^{E - 1023}

S (Sign) - 1 bit: Determines whether the number is positive (0) or negative (1).
E (Exponent) - 11 bit: The biased exponent. 1023 is subtracted to handle negative exponents in memory.
M (Mantissa) - 52 bit: Represents the significant digits (the fractional part).

The Roundoff Error

Computers have finite memory. When you enter a seemingly simple number like 0.1, its base-2 conversion generates an infinite repeating fraction (0.0001100110011...₂).

Since the mantissa only has 52 bits available for storage, the sequence is necessarily truncated. The intrinsic error in double precision is in the order of magnitude of ≈ 10^-16. This is the architectural reason why the logical operation 0.1 + 0.2 === 0.3 typically returns false in most programming languages.

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