A logarithmic analog to digital conversion method for an analog input signal includes a logarithmic amplification with progressive compression of the input signal delivering a sequence of several secondary analog signals. The trend of the values of at least some of the secondary signals is a function of the values of the analog input signal including regions corresponding to a linear trend of the secondary signals as a function of that of the input signal expressed in a logarithmic scale. The method also includes a comparison of at least some of the secondary signals of the sequence with a common reference signal whose value lies within each of regions, supplying a thermometric code information item, and a generation of a first digital word from the thermometric code information item.