1. What is 8-bit Floating Point?

The 8-bit floating point format is a compact representation of real numbers using 1 sign bit, 3 exponent bits, and 4 mantissa bits. It's useful for understanding floating point concepts and for applications where memory is extremely limited.

2. How Does the Calculator Work?

The calculator uses the floating point equation:

Where:

• \( s \) — Sign bit (0 for positive, 1 for negative)
• \( e \) — Exponent bits (0-7, bias of 3)
• \( f \) — Mantissa/fraction bits (0-7)

Explanation: The format follows IEEE-like floating point principles but with reduced precision due to fewer bits.

3. Understanding the Format

Details: The 8 bits are divided as:

• 1 sign bit (most significant bit)
• 3 exponent bits (with bias of 3)
• 4 mantissa bits (implied leading 1)

This gives a range of approximately ±0.0156 to ±30.0 with limited precision.

4. Using the Calculator

Tips: Enter any decimal number to see its 8-bit floating point representation. The calculator will show the sign, exponent, and mantissa components, the binary representation, and the reconstructed value showing the precision loss.

5. Frequently Asked Questions (FAQ)

Q1: Why is there precision loss?
A: With only 8 bits, many numbers cannot be represented exactly. The 4 mantissa bits provide only limited fractional precision.

Q2: What is the exponent bias?
A: The bias (3 in this case) allows the exponent to represent both positive and negative values while storing only positive numbers.

Q3: What's the smallest representable positive number?
A: Approximately 0.0156 (when e=0, f=1: 1.125 × 2^-6).

Q4: What's the largest representable number?
A: Approximately 30.0 (when e=6, f=7: 1.875 × 2^4).

Q5: How does this compare to IEEE 754?
A: This is a simplified version. IEEE 754 uses more bits, special values for infinity/NaN, and more sophisticated handling of denormals.