Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel with a 1-bit analog-to-digital converter (ADC) front end is investigated in the presence of correlated side information at the receiver. The design of the optimal encoder is considered for the mean squared error (MSE) distortion criterion under an average power constraint on the channel input. A necessary condition for the optimality of the encoder is derived. A numerically optimized encoder (NOE) is then obtained that aims that enforcing the necessary condition. It is observed that, due to the availability of receiver side information, the optimal encoder mapping is periodic, with its period depending on the correlation coefficient between the source and the side information. We then propose two parameterized encoder mappings, referred to as periodic linear transmission (PLT) and periodic BPSK transmission (PBT), which trade-off optimality for reduced complexity as compared to the NOE solution. We observe via numerical results that PBT performs close to the NOE in the high signal-to-noise ratio (SNR) regime, while PLT approaches the NOE performance in the low SNR regime.