diff --git a/pkg/registry/core/service/allocator/utils.go b/pkg/registry/core/service/allocator/utils.go
index baf64506e09..c034f51e6c9 100644
--- a/pkg/registry/core/service/allocator/utils.go
+++ b/pkg/registry/core/service/allocator/utils.go
@@ -24,8 +24,8 @@ import (
 // countBits returns the number of set bits in n
 func countBits(n *big.Int) int {
 	var count int = 0
-	for _, b := range n.Bytes() {
-		count += bits.OnesCount8(uint8(b))
+	for _, w := range n.Bits() {
+		count += bits.OnesCount64(uint64(w))
 	}
 	return count
 }
diff --git a/pkg/registry/core/service/allocator/utils_test.go b/pkg/registry/core/service/allocator/utils_test.go
index 4ba7dba8687..ec5c8f714eb 100644
--- a/pkg/registry/core/service/allocator/utils_test.go
+++ b/pkg/registry/core/service/allocator/utils_test.go
@@ -22,12 +22,18 @@ import (
 )
 
 func TestCountBits(t *testing.T) {
+	// bigN is an integer that occupies more than one big.Word.
+	bigN, ok := big.NewInt(0).SetString("10000000000000000000000000000000000000000000000000000000000000000", 16)
+	if !ok {
+		t.Fatal("Failed to set bigN")
+	}
 	tests := []struct {
 		n        *big.Int
 		expected int
 	}{
 		{n: big.NewInt(int64(0)), expected: 0},
 		{n: big.NewInt(int64(0xffffffffff)), expected: 40},
+		{n: bigN, expected: 1},
 	}
 	for _, test := range tests {
 		actual := countBits(test.n)
@@ -36,3 +42,13 @@ func TestCountBits(t *testing.T) {
 		}
 	}
 }
+
+func BenchmarkCountBits(b *testing.B) {
+	bigN, ok := big.NewInt(0).SetString("10000000000000000000000000000000000000000000000000000000000000000", 16)
+	if !ok {
+		b.Fatal("Failed to set bigN")
+	}
+	for i := 0; i < b.N; i++ {
+		countBits(bigN)
+	}
+}