diff --git a/barcode/codex.py b/barcode/codex.py
index b82c020..165fc4b 100755
--- a/barcode/codex.py
+++ b/barcode/codex.py
@@ -64,12 +64,14 @@ def get_fullcode(self) -> str:
         """:returns: The full code as it will be encoded."""
         return self.code
 
-    def calculate_checksum(self):
+    def calculate_checksum(self) -> str:
         check = sum(code39.MAP[x][0] for x in self.code) % 43
         for k, v in code39.MAP.items():
             if check == v[0]:
                 return k
-        return None
+        raise RuntimeError(
+            "All possible values for the checksum should have been included in the map."
+        )
 
     def build(self) -> list[str]:
         chars = [code39.EDGE]
@@ -150,7 +152,7 @@ def __init__(self, code: str, writer=None) -> None:
         self.code = code
         self.writer = writer or self.default_writer()
         self._charset = "B"
-        self._buffer = ""
+        self._digit_buffer = ""  # Accumulate pairs of digits for charset C
         check_code(self.code, self.name, code128.ALL)
 
     def __str__(self) -> str:
@@ -194,9 +196,11 @@ def look_next() -> bool:
                 codes = self._new_charset("B")
             elif char in code128.A:
                 codes = self._new_charset("A")
-            if len(self._buffer) == 1:
-                codes.append(self._convert(self._buffer[0]))
-                self._buffer = ""
+            assert self._charset != "C"
+            if len(self._digit_buffer) == 1:
+                # Flush the remaining single digit from the buffer
+                codes.append(self._convert(self._digit_buffer[0]))
+                self._digit_buffer = ""
         elif self._charset == "B":
             if look_next():
                 codes = self._new_charset("C")
@@ -209,25 +213,45 @@ def look_next() -> bool:
                 codes = self._new_charset("B")
         return codes
 
-    def _convert(self, char: str):
+    def _convert(self, char: str) -> int:
+        """Convert a character to a code number for the current charset.
+
+        NOTE: encoding digits with charset C requires buffering and is not supported
+        here. Use _convert_or_buffer instead.
+        """
         if self._charset == "A":
             return code128.A[char]
         if self._charset == "B":
             return code128.B[char]
         if self._charset == "C":
-            if char in code128.C:
+            if char in ["TO_A", "TO_B"]:
                 return code128.C[char]
-            if char.isdigit():
-                self._buffer += char
-                if len(self._buffer) == 2:
-                    value = int(self._buffer)
-                    self._buffer = ""
-                    return value
-                return None
+            raise RuntimeError("Use _convert_or_buffer for charset C.")
         raise RuntimeError(
             f"Character {char} could not be converted in charset {self._charset}."
         )
 
+    def _convert_or_buffer(self, char: str) -> int | None:
+        """Convert a character to a code number for the current charset.
+
+        If charset C is active then digits are encoded in pairs. When the first digit
+        is encountered, it is buffered and None is returned.
+        """
+        if self._charset != "C":
+            return self._convert(char)
+        if char in code128.C:
+            return code128.C[char]
+        if char.isdigit():
+            self._digit_buffer += char
+            if len(self._digit_buffer) == 1:
+                # Wait for the second digit to group in pairs
+                return None
+            assert len(self._digit_buffer) == 2
+            value = int(self._digit_buffer)
+            self._digit_buffer = ""
+            return value
+        raise RuntimeError(f"Character {char} could not be converted in charset C.")
+
     def _try_to_optimize(self, encoded: list[int]) -> list[int]:
         if encoded[1] in code128.TO:
             encoded[:2] = [code128.TO[encoded[1]]]
@@ -243,14 +267,15 @@ def _build(self) -> list[int]:
         encoded: list[int] = [code128.START_CODES[self._charset]]
         for i, char in enumerate(self.code):
             encoded.extend(self._maybe_switch_charset(i))
-            code_num = self._convert(char)
+            code_num = self._convert_or_buffer(char)
             if code_num is not None:
                 encoded.append(code_num)
-        # Finally look in the buffer
-        if len(self._buffer) == 1:
+        # If we finish in charset C with a single digit remaining in the buffer,
+        # switch to charset B and flush out the buffer.
+        if len(self._digit_buffer) == 1:
             encoded.extend(self._new_charset("B"))
-            encoded.append(self._convert(self._buffer[0]))
-            self._buffer = ""
+            encoded.append(self._convert(self._digit_buffer[0]))
+            self._digit_buffer = ""
         return self._try_to_optimize(encoded)
 
     def build(self) -> list[str]: