1. What is 32-bit Floating Point Representation?

The IEEE 754 standard defines the 32-bit floating point format that uses 1 sign bit, 8 exponent bits, and 23 mantissa bits. This format allows representation of a wide range of real numbers in computer systems.

2. How Does the Calculator Work?

The calculator uses the 32-bit floating point formula:

Where:

• \( s \) — Sign bit (0 for positive, 1 for negative)
• \( e \) — Exponent (8-bit unsigned integer)
• \( m \) — Mantissa (23-bit unsigned integer)

Explanation: The equation converts the binary representation into its decimal equivalent using the IEEE 754 standard formula.

3. Components of Floating Point

Details: The 32 bits are divided into:

• 1 sign bit (determines positive/negative)
• 8 exponent bits (with bias of 127)
• 23 mantissa bits (fractional part)

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the bias for the exponent?
A: The exponent uses a bias of 127, meaning the actual exponent is the stored value minus 127.

Q2: How are special values represented?
A: When exponent is 0 (subnormal) or 255 (infinity/NaN), special rules apply that this calculator doesn't handle.

Q3: What is the range of representable numbers?
A: Approximately ±1.18×10^-38 to ±3.4×10³⁸ for normalized numbers.

Q4: Why is there a 1 added to the mantissa?
A: This is the "hidden bit" in normalized numbers, giving 24 bits of precision while only storing 23.

Q5: How does this differ from 64-bit floating point?
A: 64-bit uses 1 sign bit, 11 exponent bits (bias 1023), and 52 mantissa bits, providing greater range and precision.