14 Bit Floating Point Calculator

14-bit Floating Point Formula:

\[ Value = (-1)^s \times (1 + f/2^7) \times 2^{(e - 15)} \]

Assumes 1 sign bit, 6 exponent bits, 7 mantissa bits for 14-bit format.

Calculated Value:

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1. What is 14-bit Floating Point Format?

The 14-bit floating point format uses 1 sign bit, 6 exponent bits, and 7 mantissa (fraction) bits. This compact representation allows storing floating-point numbers in limited space while maintaining reasonable precision.

2. How Does the Calculator Work?

The calculator uses the floating point formula:

\[ Value = (-1)^s \times (1 + f/2^7) \times 2^{(e - 15)} \]

Where:

\( s \) — Sign bit (0 for positive, 1 for negative)
\( e \) — Exponent (6 bits, 0-63)
\( f \) — Mantissa (7 bits, 0-127)
15 — Exponent bias

Explanation: The formula converts the 14-bit representation into its decimal equivalent using IEEE-like floating point principles.

3. Floating Point Representation

Details: The 14-bit format provides a trade-off between range and precision. The 6-bit exponent gives a range of about 2^-15 to 2^48, while the 7-bit mantissa provides about 3 decimal digits of precision.

4. Using the Calculator

Tips: Enter the sign bit (0 or 1), exponent (0-63), and mantissa (0-127). The calculator will compute the decimal value represented by these bits.

5. Frequently Asked Questions (FAQ)

Q1: Why use 14-bit floating point?
A: It's useful in systems with strict memory constraints where 32-bit floats would be too large.

Q2: What's the range of representable numbers?
A: Approximately ±6.1 × 10^-5 to ±2.8 × 10^14.

Q3: How does this compare to IEEE 754?
A: It's similar but with fewer bits. IEEE 754 single-precision uses 32 bits (1-8-23), while this uses 14 bits (1-6-7).

Q4: What's the exponent bias?
A: The bias is 15, meaning stored exponent = real exponent + 15.

Q5: Are there special values like NaN or infinity?
A: This simple format doesn't implement special values - all bit patterns represent regular numbers.