Fractional vs. Integer Representation
Fractional vs. Integer Representation
Fractional vs. Integer
Fractional vs. Integer
Range
Range
Integers have a maximum range
Integers have a maximum range
determined by the number of bits
determined by the number of bits
Fractions have a maximum range of ±1
Fractions have a maximum range of ±1
Precision
Precision
Integers have a maximum precision of 1
Integers have a maximum precision of 1
Fractional precision is determined by
Fractional precision is determined by
the number of bits
the number of bits
The C28x accumulator, a 32-bit register, adds extra range to integer calculations, but this
becomes a problem in storing the results back to 16-bit memory.
Conversely, when using fractions, the extra accumulator bits increase precision, which helps
minimize accumulative errors. Since any number is accurate (at best) to ± one-half of a LSB,
summing two of these values together would yield a worst case result of 1 LSB error. Four
summations produce two LSBs of error. By 256 summations, eight LSBs are “noisy.” Since the
accumulator holds 32 bits of information, and fractional results are stored from the high
accumulator, the extra range of the accumulator is a major benefit in noise reduction for long
sum-of-products type calculations.
8 - 12 C28x - Numerical Concepts & IQmath
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