1. What is 64-bit Floating Point Representation?

The 64-bit floating point format (also known as double precision) is a standard way to represent real numbers in computers. It uses 64 bits to store a numerical value with three components: sign, exponent, and mantissa.

2. How Does Floating Point Calculation Work?

The calculation follows the formula:

Where:

• \( \text{Sign} \) — Determines positive (0) or negative (1)
• \( \text{Exponent} \) — Power of 2 (biased by 1023 in actual representation)
• \( \text{Mantissa} \) — Significant digits (always between 1.0 and 2.0)

Explanation: This representation allows computers to store a wide range of values with varying precision.

3. Components of Floating Point Representation

Details: In the actual 64-bit format, the bits are allocated as follows: 1 bit for sign, 11 bits for exponent (with bias of 1023), and 52 bits for mantissa (with an implied leading 1).

4. Using the Calculator

Tips: Enter the sign (0 or 1), exponent value (-1022 to 1023), and mantissa value (1.0 to 1.999...). The calculator will compute the resulting floating point value.

5. Frequently Asked Questions (FAQ)

Q1: What is the bias in the exponent?
A: The actual exponent is stored with a bias of 1023, meaning a stored value of 1023 represents an exponent of 0.

Q2: Why is the mantissa between 1.0 and 2.0?
A: This is called normalized form, which ensures a unique representation for each number and maximizes precision.

Q3: What are special values in floating point?
A: Special values include zero, infinity, NaN (Not a Number), and denormalized numbers for very small values.

Q4: What is the precision of 64-bit floating point?
A: 64-bit floating point provides about 15-17 significant decimal digits of precision.

Q5: When would I use this calculator?
A: This calculator is useful for understanding how floating point numbers work, for educational purposes, or for verifying floating point calculations.