diff --git a/src/bitutils.py b/src/bitutils.py
index 7bd9654..aac0044 100644
--- a/src/bitutils.py
+++ b/src/bitutils.py
@@ -20,13 +20,13 @@ al = align_binary_to_left
 
 
 def shift_left(rg, fill_bit = 0):
-    return rg[1:] + fill_bit
+    return rg[1:] + str(fill_bit)
 
 l = shift_left
 
 
 def shift_right(rg, fill_bit = 0):
-    return fill_bit + rg[:-1]
+    return str(fill_bit) + rg[:-1]
 
 r = shift_right
 
@@ -37,14 +37,20 @@ def sum_supplementary_codes(x, y, size):
 sum = sum_supplementary_codes
 
 
-def sum_supplementary_codes_with_overspill(x, y, size):
+def sum_supplementary_codes_right_align(x, y, size):
+    return ar(bin(int("0b"+x, 2) + int("0b"+y, 2))[2:], size)
+
+rsum = sum_supplementary_codes_right_align
+
+
+def sum_supplementary_codes_with_overflow(x, y, size):
     result = bin(int("0b"+x, 2) + int("0b"+y, 2))[2:]
     if len(result) > size:
         return al(result, size), '1'
     else:
         return al(result, size), '0'
 
-sump = sum_supplementary_codes_with_overspill
+sump = sum_supplementary_codes_with_overflow
 
 
 def invert_bit(b):
@@ -57,3 +63,15 @@ def invert_bit(b):
         exit(1)
 
 inv = invert_bit
+
+
+def xor(x, y):
+    if len(x) == len(y):
+        result = ''
+        for i in zip(x, y):
+            if x != y:
+                result += '1'
+            else:
+                result += '0'
+
+    return result