In this work, we investigate the relationship between the dynamic range and quantization noise power in modulo analog-to-digital converters (ADCs). An algorithm to recover the original signal from quantized modulo observations with 1-bit side information is analyzed. We prove that an oversampling factor of $\mathrm{OF} > 3$ and a quantizer resolution of $b > 3$ are sufficient for the modulo ADC to have better quantization noise suppression than a standard ADC without the modulo operator. Under this setting, the mean squared error (MSE) of modulo ADC is $\mathcal{O}\left(\frac{1}{\mathrm{OF^3}}\right)$ whereas that of a standard ADC is only $\mathcal{O}\left(\frac{1}{\mathrm{OF}}\right)$. Numerical results are presented to validate the derived performance guarantees.