In this paper, the authors provides lossless data compression methodologies and compares their performance. Huffman and arithmetic coding are compare according to their performances. Data compression is a process that reduces the data size, removing the excessive information. Shorter data size is suitable because it simply reduces the cost. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing effective data density. Data compression is important application in the area of file storage and distributed system because in distributed system data have to send from and to all system. So for speed and performance efficiency data compression is used.