Log In & Log Out Code In Header

Try this code:

if(is_user_logged_in() ) {
      global $current_user;
      get_currentuserinfo();
   echo get_avatar($current_user->user_email);
    echo 'Hello, '. $current_user->display_name;
   echo '<a href="https://wordpress.stackexchange.com/wp-login.php?action=logout">logout</a>';
} else {
     echo '<a href="http://wordpress.stackexchange.com/wp-login.php?action=login">login</a>';
     echo '<a href="http://wordpress.stackexchange.com/wp-login.php?action=register">register</a>';
}