diff --git a/crates/starknet-os/src/hints/math.rs b/crates/starknet-os/src/hints/math.rs
new file mode 100644
index 00000000..565a4fd5
--- /dev/null
+++ b/crates/starknet-os/src/hints/math.rs
@@ -0,0 +1,97 @@
+use std::collections::HashMap;
+
+use cairo_vm::hint_processor::builtin_hint_processor::hint_utils::{
+    get_integer_from_var_name, insert_value_from_var_name,
+};
+use cairo_vm::hint_processor::hint_processor_definition::HintReference;
+use cairo_vm::serde::deserialize_program::ApTracking;
+use cairo_vm::types::exec_scope::ExecutionScopes;
+use cairo_vm::vm::errors::hint_errors::HintError;
+use cairo_vm::vm::vm_core::VirtualMachine;
+use cairo_vm::Felt252;
+use indoc::indoc;
+use num_bigint::BigUint;
+use num_traits::{One, Zero};
+
+use crate::hints::vars;
+
+pub const LOG2_CEIL: &str = indoc! {r#"
+	from starkware.python.math_utils import log2_ceil
+    ids.res = log2_ceil(ids.value)"#
+};
+pub fn log2_ceil_hint(
+    vm: &mut VirtualMachine,
+    _exec_scopes: &mut ExecutionScopes,
+    ids_data: &HashMap<String, HintReference>,
+    ap_tracking: &ApTracking,
+    _constants: &HashMap<String, Felt252>,
+) -> Result<(), HintError> {
+    let value = get_integer_from_var_name(vars::ids::VALUE, vm, ids_data, ap_tracking)?;
+    let res = log2_ceil(&value.to_biguint());
+    insert_value_from_var_name(vars::ids::RES, Felt252::from(res), vm, ids_data, ap_tracking)?;
+    Ok(())
+}
+
+pub fn log2_ceil(value: &BigUint) -> u64 {
+    assert!(!value.is_zero(), "log2_ceil is not defined for zero.");
+    (value - &BigUint::one()).bits()
+}
+
+#[cfg(test)]
+mod tests {
+    use cairo_vm::types::relocatable::Relocatable;
+    use num_bigint::BigUint;
+    use rstest::rstest;
+
+    use super::*;
+
+    #[rstest]
+    // Powers of two
+    #[case(1, 0)] // 1 = 2^0
+    #[case(2, 1)] // 2 = 2^1
+    #[case(4, 2)] // 4 = 2^2
+    #[case(8, 3)] // 8 = 2^3
+    #[case(1024, 10)] // 1024 = 2^10
+
+    // Non-powers of two
+    #[case(3, 2)] // between 2 and 4, floor(log2(3))=1 => log2_ceil=2
+    #[case(5, 3)] // between 4 and 8, floor(log2(5))=2 => log2_ceil=3
+    #[case(6, 3)] // between 4 and 8, floor(log2(6))=2 => log2_ceil=3
+    #[case(9, 4)] // between 8 and 16, floor(log2(9))=3 => log2_ceil=4
+    fn test_log2_ceil_parameterized(#[case] value: u64, #[case] expected: u64) {
+        let val = BigUint::from(value);
+        assert_eq!(log2_ceil(&val), expected);
+        test_log2_ceil_hint(value, expected);
+    }
+
+    #[test]
+    #[should_panic(expected = "not defined for zero")]
+    fn test_log2_ceil_zero() {
+        let zero = BigUint::from(0u64);
+        log2_ceil(&zero);
+    }
+
+    fn test_log2_ceil_hint(value: u64, expected: u64) {
+        let mut vm = VirtualMachine::new(false);
+        vm.add_memory_segment();
+        vm.add_memory_segment();
+        vm.set_fp(2);
+
+        let ap_tracking = ApTracking::new();
+        let constants = HashMap::new();
+        let ids_data = HashMap::from([
+            (vars::ids::VALUE.to_string(), HintReference::new_simple(-2)),
+            (vars::ids::RES.to_string(), HintReference::new_simple(-1)),
+        ]);
+
+        vm.insert_value(Relocatable::from((1, 0)), Felt252::from(value)).unwrap();
+
+        let mut exec_scopes: ExecutionScopes = Default::default();
+
+        log2_ceil_hint(&mut vm, &mut exec_scopes, &ids_data, &ap_tracking, &constants).unwrap();
+
+        let exp = get_integer_from_var_name(vars::ids::RES, &vm, &ids_data, &ap_tracking).unwrap();
+
+        assert_eq!(exp, Felt252::from(expected))
+    }
+}
diff --git a/crates/starknet-os/src/hints/mod.rs b/crates/starknet-os/src/hints/mod.rs
index 5452e0c1..b62ad7d4 100644
--- a/crates/starknet-os/src/hints/mod.rs
+++ b/crates/starknet-os/src/hints/mod.rs
@@ -40,6 +40,7 @@ mod execute_transactions;
 pub mod execution;
 mod find_element;
 mod kzg;
+mod math;
 mod os;
 mod output;
 mod patricia;
@@ -254,6 +255,7 @@ fn hints<PCS>() -> HashMap<String, HintImpl> where
     hints.insert(compiled_class::SET_AP_TO_SEGMENT_HASH.into(), compiled_class::set_ap_to_segment_hash);
     hints.insert(secp::READ_EC_POINT_ADDRESS.into(), secp::read_ec_point_from_address);
     hints.insert(execute_transactions::SHA2_FINALIZE.into(), execute_transactions::sha2_finalize);
+    hints.insert(math::LOG2_CEIL.into(), math::log2_ceil_hint);
     hints
 }
 
diff --git a/crates/starknet-os/src/hints/unimplemented.rs b/crates/starknet-os/src/hints/unimplemented.rs
index a55861d5..55ddb5f5 100644
--- a/crates/starknet-os/src/hints/unimplemented.rs
+++ b/crates/starknet-os/src/hints/unimplemented.rs
@@ -1,4 +1 @@
-use indoc::indoc;
-
-#[allow(unused)]
-pub const HINT_4: &str = indoc! {r#"exit_syscall(selector=ids.SHA256_PROCESS_BLOCK_SELECTOR)"#};
+// This file is intended to list all the unimplemented hints during an OS upgrade