1. What is 32-bit Floating Point?

The 32-bit single-precision floating-point format is a computer number format that occupies 4 bytes (32 bits) in computer memory. It represents a wide dynamic range of numeric values by using a floating radix point.

2. How Does the Calculator Work?

The calculator uses the IEEE 754 standard formula:

Where:

• \( s \) — Sign bit (0 for positive, 1 for negative)
• \( e \) — Exponent (8 bits, 0-255)
• \( f \) — Fraction/Mantissa (23 bits, 0-8,388,607)

Explanation: The formula breaks down the floating point number into its three components and calculates the decimal value they represent.

3. Importance of Floating Point Representation

Details: Floating-point representation allows computers to represent a much wider range of numbers than fixed-point representation, while maintaining consistent relative precision across the range.

4. Using the Calculator

Tips: Enter the sign bit (0 or 1), exponent (0-255), and fraction (0-8,388,607). The calculator will compute the decimal value represented by these components.

5. Frequently Asked Questions (FAQ)

Q1: What are special exponent values?
A: When e=0 (subnormal) and e=255 (infinity/NaN) have special meanings in IEEE 754.

Q2: What's the range of representable numbers?
A: Approximately ±1.18×10⁻³⁸ to ±3.4×10³⁸ with about 7 decimal digits of precision.

Q3: Why is there a bias of 127 in the exponent?
A: The bias allows the exponent to represent both positive and negative values without a separate sign bit.

Q4: What's the hidden bit in the mantissa?
A: The leading 1 before the binary point isn't stored (except for subnormals), which is why we add 1 to f/2²³.

Q5: How does this compare to 64-bit double precision?
A: Double precision uses 11 exponent bits (bias 1023) and 52 fraction bits, providing greater range and precision.