How to calculate an All-Pass filter quantization coefficients
Hint:


Write the transfer with a general coefficient $a$ (instead of the value $0.8$) in the numerator as well as in the denominator.
Compute the magnitude of the numerator for $z=e^{j\omega}$.
Compute the magnitude of the denominator for $z=e^{j\omega}$.
Show that both magnitudes are equal, regardless of the value of the coefficient $a$, hence $H(e^{j\omega})=1$, i.e., the system is an allpass, even after coefficient quantization.