1. What is 16-bit Floating Point?

The 16-bit floating point format (also called half-precision) is a binary floating-point 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 equation:

Where:

• \( sign \) — Sign bit (0 for positive, 1 for negative)
• \( m \) — 10-bit mantissa (0-1023)
• \( e \) — 5-bit exponent (0-31)

Explanation: The 16-bit format consists of 1 sign bit, 5 exponent bits, and 10 mantissa 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 or bandwidth is limited, such as in graphics processing, machine learning, and scientific applications where full 32-bit precision isn't required.

4. Using the Calculator

Tips: Enter the sign bit (0 or 1), mantissa (0-1023), and exponent (0-31). The calculator will compute the corresponding floating-point value.

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 float (single precision) has more range (±1.2 × 10^-38 to ±3.4 × 10^38) and about 7 decimal digits of precision.

Q3: What are common uses of 16-bit float?
A: Computer graphics (especially HDR images), neural networks, and applications where memory savings are important.

Q4: What are subnormal numbers?
A: When exponent is 0, the format uses subnormal numbers to represent values smaller than the smallest normal number.

Q5: How is infinity represented?
A: Exponent bits all 1 and mantissa 0 represents ±infinity (depending on sign bit).