Given a genome of size n, the occurrence array O requires 4 n⌉log2 n⌉ bits as each integer takes ⌈log2 n⌉ bits and there are 4 n of them in the array.
The fundamental idea is to treat the rightmost bits of an integer as representing a fraction.
In this paper it is shown that the OBDD complexity of the most significant bit of integer multiplication is exponential answering an open question posed by Wegener (2000) [18].
For each datum, the number of bits for the integer part is determined and the fractional part word-length is optimized.
The number of bits for this integer part must allow the representation of all the values taken by the data and is obtained from the data bound values.
The number of bits required for integer part is defined from the dynamic range of the data in order to avoid the occurrence of an overflow [31].
In this particular example, if the number of bits in the integer part (e.g., impl.int_bits = 2) is increased, then the user can rectify the single-pole system implementation and, for this particular word length, the verification is successfully completed.
This file contains the digital-system specification (ds), with numerator (ds.b = {1}) and denominator (ds.a = {1.0, 0.5}), and the implementation specification itself (impl), which contains the number of bits in the integer (impl.int_bits = 2) and fractional (impl.frac_bits = 4) parts, and the input range (impl.min = -1 and impl.max = 1).
On this particular case, the designer intending to implement this filter, in Direct Form I or II, would need to use an accumulator with a higher number of bits for the integer part, two's complement arithmetic, or other technique, when saturation arithmetic is employed, for preventing overflow.
The green component comes from bits 8-15 of the integer.
