Floating Point Representation

Numerical Analysis · Axiom Academy

LESSON Floating Point Representation Learn how computers store real numbers using the IEEE 754 standard Floating-point is essentially binary scientific notation . Just as we write large and small numbers in base 10 using powers of 10, computers use powers of 2. A 64-bit floating-point number (double precision) divides its bits into three parts: sign (1 bit), exponent (11 bits), and mantissa (52 bits). 3. Decoding a Floating Point Number Let's decode a real example. The number 3.14159 is stored approximately as: IEEE 754 reserves certain bit patterns for special values: zero , infinity , and NaN (Not a Number). Zero: All exponent and mantissa bits are 0 Infinity: All exponent bits are 1, mantissa is 0 NaN: All exponent bits are 1, mantissa is non-zero Denormalized: Exponent is 0, mantissa is non-zero (for very small numbers)

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