diff --git a/slither/detectors/all_detectors.py b/slither/detectors/all_detectors.py
index 4a111bb64a..97622f8878 100644
--- a/slither/detectors/all_detectors.py
+++ b/slither/detectors/all_detectors.py
@@ -94,3 +94,5 @@
 from .operations.encode_packed import EncodePackedCollision
 from .assembly.incorrect_return import IncorrectReturn
 from .assembly.return_instead_of_leave import ReturnInsteadOfLeave
+from .operations.incorrect_exp import IncorrectOperatorExponentiation
+from .statements.tautological_compare import TautologicalCompare
diff --git a/slither/detectors/operations/incorrect_exp.py b/slither/detectors/operations/incorrect_exp.py
index e69de29bb2..6188f5cb16 100644
--- a/slither/detectors/operations/incorrect_exp.py
+++ b/slither/detectors/operations/incorrect_exp.py
@@ -0,0 +1,93 @@
+"""
+Module detecting incorrect operator usage for exponentiation where bitwise xor '^' is used instead of '**'
+"""
+from typing import Tuple, List, Union
+
+from slither.core.cfg.node import Node
+from slither.core.declarations import Contract, Function
+from slither.detectors.abstract_detector import (
+    AbstractDetector,
+    DetectorClassification,
+    DETECTOR_INFO,
+)
+from slither.slithir.operations import Binary, BinaryType, Operation
+from slither.slithir.utils.utils import RVALUE
+from slither.slithir.variables.constant import Constant
+from slither.utils.output import Output
+
+
+def _is_constant_candidate(var: Union[RVALUE, Function]) -> bool:
+    """
+    Check if the variable is a constant.
+    Do not consider variable that are expressed with hexadecimal.
+    Something like 2^0xf is likely to be a correct bitwise operator
+    :param var:
+    :return:
+    """
+    return isinstance(var, Constant) and not var.original_value.startswith("0x")
+
+
+def _is_bitwise_xor_on_constant(ir: Operation) -> bool:
+    return (
+        isinstance(ir, Binary)
+        and ir.type == BinaryType.CARET
+        and (_is_constant_candidate(ir.variable_left) or _is_constant_candidate(ir.variable_right))
+    )
+
+
+def _detect_incorrect_operator(contract: Contract) -> List[Tuple[Function, Node]]:
+    ret: List[Tuple[Function, Node]] = []
+    f: Function
+    for f in contract.functions + contract.modifiers:  # type:ignore
+        # Heuristic: look for binary expressions with ^ operator where at least one of the operands is a constant, and
+        # the constant is not in hex, because hex typically is used with bitwise xor and not exponentiation
+        nodes = [node for node in f.nodes for ir in node.irs if _is_bitwise_xor_on_constant(ir)]
+        for node in nodes:
+            ret.append((f, node))
+    return ret
+
+
+# pylint: disable=too-few-public-methods
+class IncorrectOperatorExponentiation(AbstractDetector):
+    """
+    Incorrect operator usage of bitwise xor mistaking it for exponentiation
+    """
+
+    ARGUMENT = "incorrect-exp"
+    HELP = "Incorrect exponentiation"
+    IMPACT = DetectorClassification.HIGH
+    CONFIDENCE = DetectorClassification.MEDIUM
+
+    WIKI = "https://github.com/crytic/slither/wiki/Detector-Documentation#incorrect-exponentiation"
+
+    WIKI_TITLE = "Incorrect exponentiation"
+    WIKI_DESCRIPTION = "Detect use of bitwise `xor ^` instead of exponential `**`"
+    WIKI_EXPLOIT_SCENARIO = """
+```solidity
+contract Bug{
+    uint UINT_MAX = 2^256 - 1;
+    ...
+}
+```
+Alice deploys a contract in which `UINT_MAX` incorrectly uses `^` operator instead of `**` for exponentiation"""
+
+    WIKI_RECOMMENDATION = "Use the correct operator `**` for exponentiation."
+
+    def _detect(self) -> List[Output]:
+        """Detect the incorrect operator usage for exponentiation where bitwise xor ^ is used instead of **
+
+        Returns:
+            list: (function, node)
+        """
+        results: List[Output] = []
+        for c in self.compilation_unit.contracts_derived:
+            res = _detect_incorrect_operator(c)
+            for (func, node) in res:
+                info: DETECTOR_INFO = [
+                    func,
+                    " has bitwise-xor operator ^ instead of the exponentiation operator **: \n",
+                ]
+                info += ["\t - ", node, "\n"]
+                results.append(self.generate_result(info))
+
+        return results
diff --git a/slither/detectors/statements/tautological_compare.py b/slither/detectors/statements/tautological_compare.py
new file mode 100644
index 0000000000..0dc34b582f
--- /dev/null
+++ b/slither/detectors/statements/tautological_compare.py
@@ -0,0 +1,69 @@
+from typing import List
+from slither.detectors.abstract_detector import (
+    AbstractDetector,
+    DetectorClassification,
+    DETECTOR_INFO,
+)
+from slither.slithir.operations import (
+    Binary,
+    BinaryType,
+)
+
+from slither.core.declarations import Function
+from slither.utils.output import Output
+
+
+class TautologicalCompare(AbstractDetector):
+    """
+    Same variable comparison detector
+    """
+
+    ARGUMENT = "tautological-compare"
+    HELP = "Comparing a variable to itself always returns true or false, depending on comparison"
+    IMPACT = DetectorClassification.MEDIUM
+    CONFIDENCE = DetectorClassification.HIGH
+
+    WIKI = "https://github.com/crytic/slither/wiki/Detector-Documentation#tautological-compare"
+
+    WIKI_TITLE = "Tautological compare"
+    WIKI_DESCRIPTION = "A variable compared to itself is probably an error as it will always return `true` for `==`, `>=`, `<=` and always `false` for `<`, `>` and `!=`."
+    WIKI_EXPLOIT_SCENARIO = """
+```solidity
+    function check(uint a) external returns(bool){
+        return (a >= a);
+    }
+```
+`check` always return true."""
+
+    WIKI_RECOMMENDATION = "Remove comparison or compare to different value."
+
+    def _check_function(self, f: Function) -> List[Output]:
+        affected_nodes = set()
+        for node in f.nodes:
+            for ir in node.irs:
+                if isinstance(ir, Binary):
+                    if ir.type in [
+                        BinaryType.GREATER,
+                        BinaryType.GREATER_EQUAL,
+                        BinaryType.LESS,
+                        BinaryType.LESS_EQUAL,
+                        BinaryType.EQUAL,
+                        BinaryType.NOT_EQUAL,
+                    ]:
+                        if ir.variable_left == ir.variable_right:
+                            affected_nodes.add(node)
+
+        results = []
+        for n in affected_nodes:
+            info: DETECTOR_INFO = [f, " compares a variable to itself:\n\t", n, "\n"]
+            res = self.generate_result(info)
+            results.append(res)
+        return results
+
+    def _detect(self):
+        results = []
+
+        for f in self.compilation_unit.functions_and_modifiers:
+            results.extend(self._check_function(f))
+
+        return results
diff --git a/tests/e2e/detectors/test_data/tautological-compare/0.8.20/compare.sol b/tests/e2e/detectors/test_data/tautological-compare/0.8.20/compare.sol
new file mode 100644
index 0000000000..ede2f0fc18
--- /dev/null
+++ b/tests/e2e/detectors/test_data/tautological-compare/0.8.20/compare.sol
@@ -0,0 +1,6 @@
+
+contract A{
+    function check(uint a) external returns(bool){
+        return (a >= a);
+    }
+}
\ No newline at end of file
diff --git a/tests/e2e/detectors/test_data/tautological-compare/0.8.20/compare.sol-0.8.20.zip b/tests/e2e/detectors/test_data/tautological-compare/0.8.20/compare.sol-0.8.20.zip
new file mode 100644
index 0000000000..05b78fad08
Binary files /dev/null and b/tests/e2e/detectors/test_data/tautological-compare/0.8.20/compare.sol-0.8.20.zip differ
diff --git a/tests/e2e/detectors/test_detectors.py b/tests/e2e/detectors/test_detectors.py
index 9ca1bfcde9..99e9095fff 100644
--- a/tests/e2e/detectors/test_detectors.py
+++ b/tests/e2e/detectors/test_detectors.py
@@ -1664,6 +1664,16 @@ def id_test(test_item: Test):
         "incorrect_return.sol",
         "0.8.10",
     ),
+    Test(
+        all_detectors.IncorrectOperatorExponentiation,
+        "incorrect_exp.sol",
+        "0.7.6",
+    ),
+    Test(
+        all_detectors.TautologicalCompare,
+        "compare.sol",
+        "0.8.20",
+    ),
 ]
 
 GENERIC_PATH = "/GENERIC_PATH"