diff --git a/lisp/bindings.el b/lisp/bindings.el
index be44b45136..4d4411e55d 100644
--- a/lisp/bindings.el
+++ b/lisp/bindings.el
@@ -415,8 +415,8 @@ mode-line-position
               'mouse-face 'mode-line-highlight
               'help-echo "Line number and Column number\n\
 mouse-1: Display Line and Column Mode Menu")))
-       (6 ,(propertize
-	    " L%l"
+       (6 (:propertize
+	    (:eval (if (eobp) " %l" " L%l"))
 	    'local-map mode-line-column-line-number-mode-map
 	    'mouse-face 'mode-line-highlight
 	    'help-echo "Line Number\n\
diff --git a/src/xdisp.c b/src/xdisp.c
index 2aceb89c00..600fad0100 100644
--- a/src/xdisp.c
+++ b/src/xdisp.c
@@ -11579,14 +11579,19 @@ window_buffer_changed (struct window *w)
   return (BUF_SAVE_MODIFF (b) < BUF_MODIFF (b)) != w->last_had_star;
 }
 
-/* True if W has %c or %C in its mode line and mode line should be updated.  */
+/* True if W has %c or %C in its mode line and mode line should be
+   updated. or if W has %l in its mode line and point has moved either
+   to or away from EOB.  */
 
 static bool
 mode_line_update_needed (struct window *w)
 {
-  return (w->column_number_displayed != -1
-	  && !(PT == w->last_point && !window_outdated (w))
-	  && (w->column_number_displayed != current_column ()));
+  return ((w->column_number_displayed != -1
+	   && !(PT == w->last_point && !window_outdated (w))
+	   && (w->column_number_displayed != current_column ()))
+	  || (line_number_displayed
+	      && ((ZV == w->last_point && PT != ZV)
+		  || (ZV != w->last_point && PT == ZV))));
 }
 
 /* True if window start of W is frozen and may not be changed during
@@ -24395,8 +24400,13 @@ decode_mode_spec (struct window *w, register int c, int field_width,
 	line_number_displayed = true;
 
 	/* Make the string to show.  */
-	pint2str (decode_mode_spec_buf, width, topline + nlines);
-	return decode_mode_spec_buf;
+	if (PT == BUF_ZV (b))
+	  return "EOB";
+	else
+	  {
+	    pint2str (decode_mode_spec_buf, width, topline + nlines);
+	    return decode_mode_spec_buf;
+	  }
     no_value:
         {
 	  char *p = decode_mode_spec_buf;