diff --git a/crates/uplc/src/machine/error.rs b/crates/uplc/src/machine/error.rs
index bac398ca..db2d5607 100644
--- a/crates/uplc/src/machine/error.rs
+++ b/crates/uplc/src/machine/error.rs
@@ -40,7 +40,14 @@ pub enum Error {
     NotAConstant(Value),
     #[error("The evaluation never reached a final state")]
     MachineNeverReachedDone,
-
+    #[error("integerToByteString encountered negative size {0}")]
+    IntegerToByteStringNegativeSize(BigInt),
+    #[error("integerToByteString encountered negative input {0}")]
+    IntegerToByteStringNegativeInput(BigInt),
+    #[error("integerToByteString encountered size {0} which is bigger than the max size of {1}")]
+    IntegerToByteStringSizeTooBig(BigInt, i64),
+    #[error("integerToByteString encountered size {0} which is not enough space for {1} bytes")]
+    IntegerToByteStringSizeTooSmall(BigInt, usize),
     #[error("Decoding utf8")]
     Utf8(#[from] FromUtf8Error),
     #[error("Out of Bounds\n\nindex: {}\nbytestring: {}\npossible: 0 - {}", .0, hex::encode(.1), .1.len() - 1)]
diff --git a/crates/uplc/src/machine/runtime.rs b/crates/uplc/src/machine/runtime.rs
index 0d6c3604..cede5cdd 100644
--- a/crates/uplc/src/machine/runtime.rs
+++ b/crates/uplc/src/machine/runtime.rs
@@ -2,12 +2,14 @@ use std::{mem::size_of, ops::Deref, rc::Rc};
 
 use num_bigint::BigInt;
 use num_integer::Integer;
+use num_traits::{Signed, ToBytes, Zero};
 use once_cell::sync::Lazy;
 use pallas::ledger::primitives::babbage::{Language, PlutusData};
 
 use crate::{
     ast::{Constant, Data, Type},
     builtins::DefaultFunction,
+    machine::value::integer_log2,
     plutus_data_to_bytes,
 };
 
@@ -32,6 +34,8 @@ const BLST_P1_COMPRESSED_SIZE: usize = 48;
 
 const BLST_P2_COMPRESSED_SIZE: usize = 96;
 
+const INTEGER_TO_BYTE_STRING_MAXIMUM_OUTPUT_LENGTH: i64 = 8192;
+
 //#[derive(std::cmp::PartialEq)]
 //pub enum EvalMode {
 //    Immediate,
@@ -1298,6 +1302,80 @@ impl DefaultFunction {
 
                 Ok(Value::Con(constant.into()))
             }
+            DefaultFunction::IntegerToByteString => {
+                let endianness = args[0].unwrap_bool()?;
+                let size = args[1].unwrap_integer()?;
+                let input = args[2].unwrap_integer()?;
+
+                if size.is_negative() {
+                    return Err(Error::IntegerToByteStringNegativeSize(size.clone()));
+                }
+
+                if size > &INTEGER_TO_BYTE_STRING_MAXIMUM_OUTPUT_LENGTH.into() {
+                    return Err(Error::IntegerToByteStringSizeTooBig(
+                        size.clone(),
+                        INTEGER_TO_BYTE_STRING_MAXIMUM_OUTPUT_LENGTH,
+                    ));
+                }
+
+                if size.is_zero()
+                    && integer_log2(input.clone())
+                        >= 8 * INTEGER_TO_BYTE_STRING_MAXIMUM_OUTPUT_LENGTH
+                {
+                    let required = integer_log2(input.clone()) / 8 + 1;
+
+                    return Err(Error::IntegerToByteStringSizeTooBig(
+                        required.into(),
+                        INTEGER_TO_BYTE_STRING_MAXIMUM_OUTPUT_LENGTH,
+                    ));
+                }
+
+                if input.is_negative() {
+                    return Err(Error::IntegerToByteStringNegativeInput(input.clone()));
+                }
+
+                let size_unwrapped: usize = size.try_into().unwrap();
+
+                if input.is_zero() {
+                    let constant = Constant::ByteString(vec![0; size_unwrapped]);
+
+                    return Ok(Value::Con(constant.into()));
+                }
+
+                let mut bytes = if *endianness {
+                    input.to_be_bytes()
+                } else {
+                    input.to_le_bytes()
+                };
+
+                if !size.is_zero() && bytes.len() > size_unwrapped {
+                    return Err(Error::IntegerToByteStringSizeTooSmall(
+                        size.clone(),
+                        bytes.len(),
+                    ));
+                }
+
+                if size_unwrapped > 0 {
+                    let padding_size = size_unwrapped - bytes.len();
+
+                    let mut padding = vec![0; padding_size];
+
+                    if *endianness {
+                        padding.append(&mut bytes);
+
+                        bytes = padding;
+                    } else {
+                        bytes.append(&mut padding);
+                    }
+                };
+
+                let constant = Constant::ByteString(bytes);
+
+                Ok(Value::Con(constant.into()))
+            }
+            DefaultFunction::ByteStringToInteger => {
+                todo!("do it not live")
+            }
         }
     }
 }
diff --git a/crates/uplc/src/machine/value.rs b/crates/uplc/src/machine/value.rs
index 687a355a..37cac1fc 100644
--- a/crates/uplc/src/machine/value.rs
+++ b/crates/uplc/src/machine/value.rs
@@ -1,7 +1,7 @@
 use std::{collections::VecDeque, mem::size_of, ops::Deref, rc::Rc};
 
 use num_bigint::BigInt;
-use num_traits::{Signed, ToPrimitive};
+use num_traits::{Signed, ToPrimitive, Zero};
 use pallas::ledger::primitives::babbage::{self, PlutusData};
 
 use crate::{
@@ -386,8 +386,13 @@ impl TryFrom<&Value> for Constant {
     }
 }
 
-fn integer_log2(i: BigInt) -> i64 {
+pub fn integer_log2(i: BigInt) -> i64 {
+    if i.is_zero() {
+        return 0;
+    }
+
     let (_, bytes) = i.to_bytes_be();
+
     match bytes.first() {
         None => unreachable!("empty number?"),
         Some(u) => (8 - u.leading_zeros() - 1) as i64 + 8 * (bytes.len() - 1) as i64,
@@ -524,6 +529,7 @@ mod tests {
     #[test]
     fn integer_log2_oracle() {
         // Values come from the Haskell implementation
+        assert_eq!(integer_log2(0.into()), 0);
         assert_eq!(integer_log2(1.into()), 0);
         assert_eq!(integer_log2(42.into()), 5);
         assert_eq!(