This work presents a comprehensive study of the properties of finite (0,1) binary systems from the mathematical viewpoint of quantum theory where a complex wavefunction $ψ_{n}$ is considered as an analogous probability measure. This is a quantum-inspired extension of the GenomeBits model to characterise observed genome sequences, where $ψ_{n}$ is related to an alternating (0,1) binary series having independent distributed terms. The real and imaginary spectrum of $ψ_{n}$ {\emph vs.} the nucleotide base positions display characteristic features of sound waves.