The increasing demand for low-cost and low-power radars has led to the emergence of 1-bit sampling technology. 1-bit sampling technology is introduced in a multiple-input and multiple-output (MIMO) radar that has many advantages such as a high degree of freedom and flexible transmit beam pattern. The authors' theoretical derivation shows that after 1-bit quantisation, the received signal can be expressed as a linear combination of infinite components, which include the original component and high-order components that can be regarded as interference terms. On this basis, the signal-tonoise-ratio (SNR) loss after 1-bit sampling at a low SNR is 1.96 dB. Furthermore, the Cramér-Rao bound (CRB) of a MIMO radar with 1-bit sampling is derived. In the derivation, the concept of 1-bit equivalent noise is proposed. At low SNRs, the equivalent noise power is π/2 (1.96 dB) times the original noise power, which is consistent with a previous derivation. Numerical simulations showed the feasibility of traditional algorithms for a MIMO radar with 1-bit sampling and the correctness of the authors' derivation.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.