diff --git a/sympy/combinatorics/graycode.py b/sympy/combinatorics/graycode.py
index 8e67f587954a..8c84868f5c5c 100644
--- a/sympy/combinatorics/graycode.py
+++ b/sympy/combinatorics/graycode.py
@@ -362,8 +362,8 @@ def bin_to_gray(bin_list):
     gray_to_bin
     """
     b = [bin_list[0]]
-    for i in range(0, len(bin_list) - 1):
-        b += str(int(bin_list[i]) ^ int(b[i - 1]))
+    for i in range(1, len(bin_list)):
+        b += str(int(bin_list[i]) ^ int(bin_list[i - 1]))
     return ''.join(b)
 
 
diff --git a/sympy/combinatorics/tests/test_graycode.py b/sympy/combinatorics/tests/test_graycode.py
index d67e97d31610..8864a8b9ce6b 100644
--- a/sympy/combinatorics/tests/test_graycode.py
+++ b/sympy/combinatorics/tests/test_graycode.py
@@ -1,5 +1,6 @@
 from sympy.combinatorics.graycode import (GrayCode, bin_to_gray,
-    random_bitstring, get_subset_from_bitstring, graycode_subsets)
+    random_bitstring, get_subset_from_bitstring, graycode_subsets,
+    gray_to_bin)
 
 
 def test_graycode():
@@ -55,3 +56,9 @@ def test_graycode():
     assert list(graycode_subsets(['a', 'b', 'c'])) == \
         [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'],
     ['a', 'c'], ['a']]
+
+def test_live_issue_117():
+    assert bin_to_gray('0100') == '0110'
+    assert bin_to_gray('0101') == '0111'
+    for bits in ('0100', '0101'):
+        assert gray_to_bin(bin_to_gray(bits)) == bits