The
floating-point representation of any number consists of three fields known as Sign, Exponent and Significant or Mantissa part.
A reasonable upper bound p = 27 resembles the equality of the number of fractional bits [p.sub.f] = 23 to the number of bits in the fractional part f of the single-precision binary
floating-point representation, which is the smallest precision used in most software implementations.
Among the topics are mathematical preliminaries and
floating-point representation, numerical integration, least squares methods and Fourier series, boundary-value problems, and linear programming problems.
If students are not aware of 64-bit
floating-point representation at this point in their study, then the next step usually involves the default 32-bit
floating-point representation.
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Floating-point representation of data has a smaller amount of probable error and noise.
One could imagine a hypothetical machine that used IEEE
floating-point representation, but to save transistors sometimes mangled the low-order bits of the mantissa.
The concern is about scientific applications using
floating-point representation, and justifiably so.
2 A common definition of the relative machine precision, or unit roundoff, is the smallest positive floating-point value, [Epsilon], such that fl(1 + [Epsilon]) [greater than] 1, where fl(x) is the
floating-point representation of x.