Logarithmic CMOS image sensors are easily able, at video rates, to capture scenes where the dynamic range (DR) is high. However, tone mapping is required to output resulting images or videos to standard low-DR displays. This article proposes a new method, designed especially for logarithmic CMOS image sensors, which can suffer from temporal, and residual fixed pattern, noise. The novel tone mapping, a global operator based on histogram adjustment, uses a model of the camera noise to ensure that the mapping does not amplify the noise above a display threshold. Moreover, to reduce the likelihood of flickering, a temporal adaptation process is incorporated into the histogram calculation. Furthermore, to reduce complexity for real-time processing, a fixed-point implementation is designed for the proposed tone mapping. The novel operator and its fixed-point design are validated through offline and real-time experiments with a logarithmic CMOS image sensor.