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Today lets discuss about 32-bit (FP32) and 16-bit (FP16) floating-point!
Floating-point numbers are used to represent real numbers (like decimals) and they consist of three parts:
32-bit Floating Point (FP32)
Total bits: 32 bits
Sign bit: 1 bit
Exponent: 8 bits
Mantissa: 23 bits
For example:
A number like -15.375 would be represented as:
Sign bit: 1 (negative number)
Exponent: Stored after being adjusted by a bias (127 in FP32).
Mantissa: The significant digits after converting the number to binary.
16-bit Floating Point (FP16)
Total bits: 16 bits
Sign bit: 1 bit
Exponent: 5 bits
Mantissa: 10 bits
Example:
A number like -15.375 would be stored similarly:
Sign bit: 1 (negative number)
Exponent: Uses 5 bits, limiting the range compared to FP32.
Mantissa: Only 10 bits for precision.
Precision and Range
FP32: Higher precision and larger range, with about 7 decimal places of accuracy.
FP16: Less precision (around 3-4 decimal places), smaller range but faster computations and less memory use.
Floating-point numbers are used to represent real numbers (like decimals) and they consist of three parts:
Sign bit:
Indicates whether the number is positive (0) or negative (1).
Exponent:
Determines the scale of the number (i.e., how large or small it is by shifting the decimal point).
Mantissa (or fraction):
Represents the actual digits of the number.32-bit Floating Point (FP32)
Total bits: 32 bits
Sign bit: 1 bit
Exponent: 8 bits
Mantissa: 23 bits
For example:
A number like -15.375 would be represented as:
Sign bit: 1 (negative number)
Exponent: Stored after being adjusted by a bias (127 in FP32).
Mantissa: The significant digits after converting the number to binary.
16-bit Floating Point (FP16)
Total bits: 16 bits
Sign bit: 1 bit
Exponent: 5 bits
Mantissa: 10 bits
Example:
A number like -15.375 would be stored similarly:
Sign bit: 1 (negative number)
Exponent: Uses 5 bits, limiting the range compared to FP32.
Mantissa: Only 10 bits for precision.
Precision and Range
FP32: Higher precision and larger range, with about 7 decimal places of accuracy.
FP16: Less precision (around 3-4 decimal places), smaller range but faster computations and less memory use.
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