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Half Precision Float Formula:
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Half-precision floating-point (float16) is a binary floating-point computer number format that occupies 16 bits (2 bytes) in computer memory. It's used when memory bandwidth or storage is at a premium, such as in machine learning applications and graphics processing.
The calculator uses the half-precision float formula:
Where:
Explanation: The formula converts the 16-bit representation into its decimal equivalent, accounting for sign, fraction, and exponent components.
Details: Half-precision floats provide a good balance between precision and storage efficiency. They are widely used in applications where reduced memory usage and bandwidth are more important than full precision, such as in deep neural networks and computer graphics.
Tips: Enter the sign bit (0 or 1), fraction (0-1023), and exponent (0-31) values. The calculator will compute the decimal equivalent of the half-precision float representation.
Q1: What's the range of half-precision floats?
A: Approximately ±6.1 × 10^-5 to ±6.5 × 10^4 with about 3-4 decimal digits of precision.
Q2: When should I use half-precision?
A: When memory or bandwidth is limited, and reduced precision is acceptable, such as in machine learning inference or certain graphics applications.
Q3: What are the special cases in half-precision?
A: Values when exponent is 0 (subnormal numbers) or 31 (infinity/NaN) have special interpretations.
Q4: How does this compare to single and double precision?
A: Half-precision (16-bit) has less range and precision than single (32-bit) or double (64-bit) precision floats.
Q5: Can I convert decimal numbers to half-precision?
A: Yes, but this calculator only converts from half-precision components to decimal. Full conversion would require more complex rounding logic.