diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/BinaryOp/NonDivArithmeticOpAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/Expression/BinaryOp/NonDivArithmeticOpAnalyzer.php
index c26fa7ca6ef..83d11e83b48 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/BinaryOp/NonDivArithmeticOpAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/BinaryOp/NonDivArithmeticOpAnalyzer.php
@@ -663,7 +663,15 @@ private static function analyzeNonDivOperands(
                     if ($parent instanceof PhpParser\Node\Expr\BinaryOp\Minus) {
                         $always_positive = false;
                     } elseif ($left_is_positive && $right_is_positive) {
-                        $always_positive = true;
+                        if ($parent instanceof PhpParser\Node\Expr\BinaryOp\BitwiseXor
+                            || $parent instanceof PhpParser\Node\Expr\BinaryOp\BitwiseAnd
+                            || $parent instanceof PhpParser\Node\Expr\BinaryOp\ShiftLeft
+                            || $parent instanceof PhpParser\Node\Expr\BinaryOp\ShiftRight
+                        ) {
+                            $always_positive = false;
+                        } else {
+                            $always_positive = true;
+                        }
                     } elseif ($parent instanceof PhpParser\Node\Expr\BinaryOp\Plus
                         && ($left_type_part instanceof TLiteralInt && $left_type_part->value === 0)
                         && $right_is_positive
diff --git a/tests/BinaryOperationTest.php b/tests/BinaryOperationTest.php
index cb898886f7d..d46ef20f1f7 100644
--- a/tests/BinaryOperationTest.php
+++ b/tests/BinaryOperationTest.php
@@ -357,6 +357,37 @@ function onlyZeroOrPlusMinusOne(int $i): int {
                      function foo($a, $b): void {
                          onlyZeroOrPlusMinusOne($a <=> $b);
                      }'
+            ],
+            'notAlwaysPositiveBitOperations' => [
+                '<?php
+
+                    $a = 1;
+                    $b = 1;
+                    $c = 32;
+                    $d = 64;
+                    $e = 2;
+
+                    if (0 === ($a ^ $b)) {
+                        echo "Actually, zero\n";
+                    }
+
+                    if (0 === ($a & $e)) {
+                        echo "Actually, zero\n";
+                    }
+
+                    if (0 === ($a >> $b)) {
+                        echo "Actually, zero\n";
+                    }
+
+                    if (8 === PHP_INT_SIZE) {
+                        if (0 === ($a << $d)) {
+                            echo "Actually, zero\n";
+                        }
+                    } else {
+                        if (0 === ($a << $c)) {
+                            echo "Actually, zero\n";
+                        }
+                    }'
             ]
         ];
     }