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 ψn is considered as an analogous probability measure. This is a quantum-inspired extension of the GenomeBits model to characterise observed genome sequences, where ψn is related to an alternating (0,1) binary series having independent distributed terms. The real and imaginary spectrum of ψn v s. the nucleotide base positions display characteristic features of sound waves.