A fractional folding analog-to-digital converter (ADC) with a novel arithmetic digital encoding technique is discussed. In order to reduce the asymmetry errors of the boundary conditions for the conventional folding ADC, a structure using an odd number of folding blocks and fractional folding rate is proposed. To implement the fractional technique, a new arithmetic digital encoding technique composed of a memory and an adder is described. Further, the coding errors generated by device mismatching and other external factors are minimized, since an iterating offset self-calibration technique is adopted with a digital error correction logic. A prototype 8-bit 1GS/s ADC has been fabricated using an 1.2V 0.13 um 1-poly 6-metal CMOS process. The effective chip area is $2.1mm^2$(ADC core : $1.4mm^2$, calibration engine : $0.7mm^2$), and the power consumption is 88 mW. The measured SNDR is 46.22 dB at the conversion rate of 1 GS/s. Both values of INL and DNL are within 1 LSB.