A PCM signal processor which converts an analog signal into a digital signal to transmit or record the digital signal. When the PCM signal processor receives a PCM signal whose data has been compressed in such a manner that one or more lower bits are cut off from a plurality of bits for forming the PCM signal and indicating the signal level of the analog signal, in accordance with the signal level of the analog signal, one or more bits corresponding to the number of bits having been cut off are added in the processor to the compressed PCM signal at the position following the least significant bit of the compressed PCM signal. Correction data indicating about one half the largest one of numerical values that can be expressed by the added bit or bits, is given to the added bit or bits.