A signal chain model of single-bit and multi-bit quanta image sensors (QISs) is established. Based on the proposed model, the photoresponse characteristics and signal error rates of QISs are investigated, and the effects of bit depth, quantum efficiency, dark current, and read noise on them are analyzed. When the signal error rates towards photons and photoelectrons counting are lower than 0.01, the high accuracy photon and photoelectron counting exposure ranges are determined. Furthermore, an optimization method of integration time to ensure that the QIS works in these high accuracy exposure ranges is presented. The trade-offs between pixel area, the mean value of incident photons, and integration time under different illuminance level are analyzed. For the 3-bit QIS with 0.16 e-/s dark current and 0.21 e- r.m.s. read noise, when the illuminance level and pixel area are 1 lux and 1.21 μm², or 10 000 lux and 0.21 μm², the recommended integration time is 8.8 to 30 ms, or 10 to 21.3 μs, respectively. The proposed method can guide the design and operation of single-bit and multi-bit QISs.