Abstract 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‐to‐noise‐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.