Double Floating Point Calculator

Double Precision Floating Point Representation:

\[ \text{double} = \text{sign} \times \text{mantissa} \times 2^{\text{exp}} \]

Double Precision Value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Double Precision Floating Point?

Double precision floating point is a 64-bit format for representing real numbers in computers. It consists of 1 sign bit, 11 exponent bits, and 52 mantissa bits, providing about 15-17 significant decimal digits of precision.

2. How Does the Calculator Work?

The calculator uses the double precision formula:

\[ \text{double} = \text{sign} \times \text{mantissa} \times 2^{\text{exp}} \]

Where:

\( \text{sign} \) — 0 (positive) or 1 (negative)
\( \text{mantissa} \) — 52-bit fractional part (with implicit leading 1)
\( \text{exp} \) — Exponent (bias of 1023 in actual representation)

Explanation: The calculator converts the binary mantissa to a decimal fraction, adds the implicit leading 1, and applies the sign and exponent to compute the final value.

3. Importance of Floating Point Representation

Details: Understanding floating point representation is crucial for numerical computing, scientific calculations, and avoiding rounding errors in financial or precision-critical applications.

4. Using the Calculator

Tips: Enter the sign bit (0 or 1), up to 52 binary digits for the mantissa, and an exponent between -1022 and 1023. The calculator will show the decimal equivalent of the floating point number.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between single and double precision?
A: Single precision uses 32 bits (1 sign, 8 exponent, 23 mantissa) while double uses 64 bits (1 sign, 11 exponent, 52 mantissa), providing more precision and range.

Q2: What is the exponent bias?
A: In actual representation, the exponent is stored with a bias of 1023 (for double precision) to allow both positive and negative exponents.

Q3: What are special values in floating point?
A: Special values include ±0, ±infinity, denormal numbers, and NaN (Not a Number) for undefined operations.

Q4: Why is there an implicit leading 1?
A: The leading 1 is implicit (not stored) in normal numbers to gain an extra bit of precision in the mantissa.

Q5: What are common floating point pitfalls?
A: Rounding errors, non-associativity of operations, and loss of precision when subtracting nearly equal numbers.