In this paper, we propose a learning method of multi-layer perceptrons (MLPs) with 8-bit data precision. The suggested method uses the cross-entropy cost function to remove the slope term of error signal in output layer. To decrease the possibility of overflows, we use 16-bit weighted sum results into the 8-bit data with appropriate range. In the forwared propagation, the range for bit-conversion is determined using the saturation property of sigmoid function. In the backwared propagation, the range for bit-conversion is derived using the probability density function of back-propagated signal. In a simulation study to classify hadwritten digits in the CEDAR database, our method shows similar generalization performance to the error back-propagation learning with 16-bit precision.