FileInfo fi = new FileInfo(fullpath);
String b64ZippedData = String.Empty;
using (FileStream filestream = fi.OpenRead()) // source
{
    using (MemoryStream memorystream = new MemoryStream()) // destination
    {
        using (GZipStream gzipstream = new GZipStream(memorystream, CompressionMode.Compress, false)) // compression engine
        {
            filestream.CopyTo(gzipstream);
        }
        b64ZippedData = System.Convert.ToBase64String(memorystream.ToArray());
    }
}