diff --git a/reasoning_gym/algorithmic/base_conversion.py b/reasoning_gym/algorithmic/base_conversion.py
index eb0978bd..c1f62654 100644
--- a/reasoning_gym/algorithmic/base_conversion.py
+++ b/reasoning_gym/algorithmic/base_conversion.py
@@ -60,14 +60,34 @@ class BaseConversionDataset(ProceduralDataset):
         value, source_base, target_base = self._generate_conversion(rng)
 
         # Convert decimal to source base representation
-        source_repr = format(value, f"x" if source_base == 16 else f"b" if source_base == 2 else "").strip()
-        if source_base not in (2, 16):
-            source_repr = format(value, f"{source_base}x").lower().strip()
+        if source_base == 16:
+            source_repr = format(value, 'x')
+        elif source_base == 2:
+            source_repr = format(value, 'b')
+        else:
+            # Manual conversion for other bases
+            n = value
+            digits = []
+            while n:
+                digits.append(int(n % source_base))
+                n //= source_base
+            source_repr = ''.join(str(d) if d < 10 else chr(ord('a') + d - 10) 
+                                for d in reversed(digits) or [0])
 
         # Convert decimal to target base for answer
-        target_repr = format(value, f"x" if target_base == 16 else f"b" if target_base == 2 else "").strip()
-        if target_base not in (2, 16):
-            target_repr = format(value, f"{target_base}x").lower().strip()
+        if target_base == 16:
+            target_repr = format(value, 'x')
+        elif target_base == 2:
+            target_repr = format(value, 'b')
+        else:
+            # Manual conversion for other bases
+            n = value
+            digits = []
+            while n:
+                digits.append(int(n % target_base))
+                n //= target_base
+            target_repr = ''.join(str(d) if d < 10 else chr(ord('a') + d - 10) 
+                                for d in reversed(digits) or [0])
 
         source_name = self._format_base_name(source_base)
         target_name = self._format_base_name(target_base)
diff --git a/tests/test_base_conversion.py b/tests/test_base_conversion.py
index 7c8edf1e..dced77c4 100644
--- a/tests/test_base_conversion.py
+++ b/tests/test_base_conversion.py
@@ -83,6 +83,32 @@ def test_base_conversion_dataset_iteration():
     assert items == list(dataset)
 
 
+def test_base_conversion_validity():
+    """Test that generated numbers are valid for their bases"""
+    config = BaseConversionConfig(
+        min_base=2,
+        max_base=36,
+        min_value=0,
+        max_value=1000,
+        size=100,
+        seed=42
+    )
+    dataset = BaseConversionDataset(config)
+
+    def is_valid_for_base(num_str: str, base: int) -> bool:
+        valid_chars = "0123456789abcdefghijklmnopqrstuvwxyz"[:base]
+        return all(c in valid_chars for c in num_str.lower())
+
+    for i in range(len(dataset)):
+        item = dataset[i]
+        assert is_valid_for_base(item["metadata"]["source_repr"], 
+                               item["metadata"]["source_base"]), \
+            f"Invalid source number {item['metadata']['source_repr']} for base {item['metadata']['source_base']}"
+        assert is_valid_for_base(item["metadata"]["target_repr"], 
+                               item["metadata"]["target_base"]), \
+            f"Invalid target number {item['metadata']['target_repr']} for base {item['metadata']['target_base']}"
+
+
 def test_base_conversion_special_bases():
     """Test conversion between special bases (binary, hex)"""
     config = BaseConversionConfig(