For an AGWN channel, based on Log-MAP decoding algorithm, quantization and fixed-point number representation of all the data which are produced during the SISO iterative decoding of turbo codes are analyzed and studied systematically. According to data observation and anatomy of algorithm, with Monte Carlo simulation, this paper presents the fixed-point representations and quatization details of the data such as received information, extrinsic information, the channel reliability value, state metric, etc. By the quatization scheme determined in this paper a better tradeoff between the decoding performance and implementation complexity can be obtained, and the degradation of performance is not more than 0.15 dB.