Low-resolution quantization constrains the maximum achievable gains of multiple-input multiple-output (MIMO) systems. While the adverse effects and mitigation strategies have been thoroughly analyzed for communication systems, the impact of low-resolution quantization on integrated sensing and communication (ISAC) systems remains insufficiently explored in the existing literature. In this paper, we propose an analysis and design framework to investigate and mitigate the effects of 1-bit digital to analog converters (DACs) for ISAC systems. Firstly, an analytical sensing signal-to-noise ratio (SNR) expression is derived by using the Bussgang decomposition. Furthermore, two different methodologies are proposed to design a transmit waveform that satisfies both communication and sensing requirements simultaneously. The first method uses a separate constant modulus (CM) sensing signal since CM signals are known to be more robust to nonlinear distortion than orthogonal frequency division multiplexing (OFDM) modulated signals. The second method employs the squared-infinity norm Douglas-Rachford splitting (SQUID) approach to construct the transmit waveform using nonlinear quantized precoding. Finally, the performance of the proposed methods are validated via numerical simulations to indicate the complexity-performance tradeoff between two different methods.