An analog/digital gain control device avoid some of the requirements associated with the nature of a closed-loop AGC circuits and which meets the remaining requirements without much difficulty uses an analog to digital conversion method that increases the number of effective ADC bits by compressing the baseband input analog signal using a logarithmic circuit. After the compressed analog signal is converted into a digital signal, a digital anti-log process or look-up table (LUT) is used to expand the digital signal back to the original linear scale. The word size of the output of the anti-log process is larger than the input word size due to the nature of the anti-log function. To reduce the word size of the digital signal an open loop normalization technique can be applied.