Single Precision Floating Point Calculator

Single Precision Formula:

\[ \text{single} = \text{sign} \times (1 + \frac{m}{2^{23}}) \times 2^{e-127} \]

Single Precision Value:

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1. What is Single Precision Floating Point?

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

2. How Does the Calculator Work?

The calculator uses the single precision formula:

\[ \text{single} = \text{sign} \times (1 + \frac{m}{2^{23}}) \times 2^{e-127} \]

Where:

\( sign \) — Sign bit (0 for positive, 1 for negative)
\( m \) — Mantissa (23-bit fraction part)
\( e \) — Exponent (8-bit biased exponent)

Explanation: The formula converts the binary representation of a single-precision float into its decimal equivalent.

3. Importance of Floating Point Representation

Details: Understanding floating-point representation is crucial for computer scientists, numerical analysts, and anyone working with scientific computing or graphics programming.

4. Using the Calculator

Tips: Enter the sign bit (0 or 1), mantissa (0 to 8,388,607), and exponent (0 to 255). The calculator will compute the corresponding single-precision floating-point value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between single and double precision?
A: Single precision uses 32 bits (about 7 decimal digits), while double precision uses 64 bits (about 16 decimal digits).

Q2: What are special exponent values?
A: Exponent 0 (with mantissa 0) represents ±0. Exponent 255 represents ±infinity or NaN (Not a Number).

Q3: What's the range of single precision?
A: Approximately ±1.18×10^-38 to ±3.4×10³⁸.

Q4: Why is the exponent biased?
A: The bias (127) allows representation of both positive and negative exponents without a separate sign bit.

Q5: What about denormal numbers?
A: When exponent is 0, the formula changes to 0.m × 2^-126 for denormal (subnormal) numbers.