1. What is Floating Point to Decimal Conversion?

Floating point to decimal conversion is the process of converting a binary floating point number (as stored in computer memory) to its exact decimal representation. This is important for understanding the precise value stored in floating point variables.

2. How Does the Calculator Work?

The calculator uses the IEEE 754 floating point standard:

Where:

• \( sign \) — Determines positive/negative (0/1)
• \( mantissa \) — Fractional part of the number
• \( exponent \) — Power of 2 multiplier
• \( bias \) — 127 for 32-bit, 1023 for 64-bit

Explanation: The calculator converts the binary representation back to its exact decimal equivalent, showing the precise value stored in memory.

3. Importance of Floating Point Conversion

Details: Understanding floating point representation helps debug numerical precision issues, validate calculations, and ensure accurate financial or scientific computations.

4. Using the Calculator

Tips: Enter any floating point number and select precision (32-bit for single precision, 64-bit for double precision). The calculator will show the exact decimal representation stored in memory.

5. Frequently Asked Questions (FAQ)

Q1: Why don't floating point numbers store exact decimal values?
A: Floating point uses binary fractions which can't precisely represent all decimal fractions, leading to rounding errors.

Q2: What's the difference between 32-bit and 64-bit floating point?
A: 32-bit (single precision) has about 7 decimal digits of precision, while 64-bit (double) has about 16 digits.

Q3: Why does 0.1 + 0.2 not equal 0.3 exactly?
A: Neither 0.1 nor 0.2 can be represented exactly in binary floating point, causing small rounding errors.

Q4: When should I use this converter?
A: When you need to verify the exact value stored in a floating point variable or debug precision issues.

Q5: How can I avoid floating point precision problems?
A: For financial calculations, use decimal arithmetic libraries instead of native floating point.