The present invention relates to a modulation and demodulation method of minimizing an error rate and applying it to a differential operation modulo 4. A modulation apparatus includes a Gray coding circuit 101 to which data of (2n+1) bits are inputted (where “n” is an integer more than 1) and which encodes 2 bits of an input signal of (2n+1) bits to a Gray code as a signal for allowing four quadrants to be identified, an encoding circuit 102 that encodes 3 bits of the input signal of (2n+1) bits as a signal indicating any one of eight subgroups provided in each of the four quadrants so that an average Hamming distance between adjacent subgroups within its quadrant becomes a minimum, and a mapping circuit 104 that maps binary data encoded by the Gray coding circuit 101 and the encoding circuit 102 on the four quadrants.