1. What is 16-bit Floating Point?

16-bit floating point (also called half-precision) is a computer number format that occupies 16 bits (2 bytes) in computer memory. It follows the IEEE 754 standard for floating-point arithmetic.

2. How Does the Calculator Work?

The calculator uses the 16-bit floating point formula:

Where:

• \( s \) — Sign bit (0 for positive, 1 for negative)
• \( f \) — Fraction part (10 bits, 0-1023)
• \( e \) — Exponent part (5 bits, 0-31)

Explanation: The format consists of 1 sign bit, 5 exponent bits, and 10 fraction bits. The exponent is stored with a bias of 15.

3. Importance of 16-bit Floating Point

Details: Half-precision floating point is used when memory storage is at a premium, such as in graphics processing, machine learning applications, and embedded systems.

4. Using the Calculator

Tips: Enter the sign bit (0 or 1), fraction (0-1023), and exponent (0-31). The calculator will compute the decimal value represented by these bits.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of 16-bit floating point?
A: Approximately ±6.1×10^-5 to ±6.5×10^4 with about 3-4 decimal digits of precision.

Q2: How does this compare to 32-bit float?
A: 32-bit single-precision has about 7 decimal digits of precision and much wider range, but uses twice the memory.

Q3: When should I use 16-bit float?
A: When memory bandwidth is more important than precision, such as in large datasets where precision isn't critical.

Q4: What about special values like infinity or NaN?
A: The exponent field 31 (all 1s) is reserved for infinities and NaNs, which this calculator doesn't handle.

Q5: What's the smallest positive normal number?
A: When e=1 and f=0: 2^-14 ≈ 6.1×10^-5