diff --git a/gadgets/src/errors/signed_integer.rs b/gadgets/src/errors/signed_integer.rs
index 6cee056445..a819966ef0 100644
--- a/gadgets/src/errors/signed_integer.rs
+++ b/gadgets/src/errors/signed_integer.rs
@@ -2,6 +2,9 @@ use snarkos_errors::gadgets::SynthesisError;
 
 #[derive(Debug, Error)]
 pub enum IntegerError {
+    #[error("Negative zero")]
+    NegativeZero,
+
     #[error("Integer overflow")]
     Overflow,
 
diff --git a/gadgets/src/signed_integer/arithmetic/add.rs b/gadgets/src/signed_integer/arithmetic/add.rs
index e6be0fcef6..dd1c12955c 100644
--- a/gadgets/src/signed_integer/arithmetic/add.rs
+++ b/gadgets/src/signed_integer/arithmetic/add.rs
@@ -11,7 +11,7 @@ use snarkos_models::{
     },
 };
 
-/// Modular addition for a signed integer gadget
+/// Addition for a signed integer gadget
 pub trait Add<Rhs = Self>
 where
     Self: std::marker::Sized,
diff --git a/gadgets/src/signed_integer/arithmetic/div.rs b/gadgets/src/signed_integer/arithmetic/div.rs
index 80d45e8ece..5412577cec 100644
--- a/gadgets/src/signed_integer/arithmetic/div.rs
+++ b/gadgets/src/signed_integer/arithmetic/div.rs
@@ -1,7 +1,7 @@
 use crate::{errors::IntegerError, Int16, Int32, Int64, Int8};
 use snarkos_models::{curves::PrimeField, gadgets::r1cs::ConstraintSystem};
 
-/// Modular division for a signed integer gadget
+/// Division for a signed integer gadget
 pub trait Div<Rhs = Self>
 where
     Self: std::marker::Sized,
diff --git a/gadgets/src/signed_integer/arithmetic/mod.rs b/gadgets/src/signed_integer/arithmetic/mod.rs
index a7a64be042..ae4970b62e 100644
--- a/gadgets/src/signed_integer/arithmetic/mod.rs
+++ b/gadgets/src/signed_integer/arithmetic/mod.rs
@@ -8,6 +8,9 @@ pub use self::div::*;
 pub mod mul;
 pub use self::mul::*;
 
+pub mod twos_complement;
+pub use self::twos_complement::*;
+
 pub mod pow;
 pub use self::pow::*;
 
diff --git a/gadgets/src/signed_integer/arithmetic/mul.rs b/gadgets/src/signed_integer/arithmetic/mul.rs
index 275bdb9a6b..03b9b46b08 100644
--- a/gadgets/src/signed_integer/arithmetic/mul.rs
+++ b/gadgets/src/signed_integer/arithmetic/mul.rs
@@ -1,7 +1,7 @@
 use crate::{errors::IntegerError, Int16, Int32, Int64, Int8};
 use snarkos_models::{curves::PrimeField, gadgets::r1cs::ConstraintSystem};
 
-/// Modular multiplication for a signed integer gadget
+/// Multiplication for a signed integer gadget
 pub trait Mul<Rhs = Self>
 where
     Self: std::marker::Sized,
diff --git a/gadgets/src/signed_integer/arithmetic/pow.rs b/gadgets/src/signed_integer/arithmetic/pow.rs
index 95f92c7083..d08dacf073 100644
--- a/gadgets/src/signed_integer/arithmetic/pow.rs
+++ b/gadgets/src/signed_integer/arithmetic/pow.rs
@@ -1,7 +1,7 @@
 use crate::{errors::IntegerError, Int16, Int32, Int64, Int8};
 use snarkos_models::{curves::PrimeField, gadgets::r1cs::ConstraintSystem};
 
-/// Modular exponentiation for a signed integer gadget
+/// Exponentiation for a signed integer gadget
 pub trait Pow<Rhs = Self>
 where
     Self: std::marker::Sized,
diff --git a/gadgets/src/signed_integer/arithmetic/sub.rs b/gadgets/src/signed_integer/arithmetic/sub.rs
index ecf0a46d2a..04baf70a53 100644
--- a/gadgets/src/signed_integer/arithmetic/sub.rs
+++ b/gadgets/src/signed_integer/arithmetic/sub.rs
@@ -1,7 +1,7 @@
-use crate::{errors::IntegerError, Int16, Int32, Int64, Int8};
+use crate::{errors::IntegerError, Int128, Int16, Int32, Int64, Int8};
 use snarkos_models::{curves::PrimeField, gadgets::r1cs::ConstraintSystem};
 
-/// Modular subtraction for a signed integer gadget
+/// Subtraction for a signed integer gadget
 pub trait Sub<Rhs = Self>
 where
     Self: std::marker::Sized,
@@ -20,4 +20,4 @@ macro_rules! sub_int_impl {
     )*)
 }
 
-sub_int_impl!(Int8 Int16 Int32 Int64);
+sub_int_impl!(Int8 Int16 Int32 Int64 Int128);
diff --git a/gadgets/src/signed_integer/arithmetic/twos_complement.rs b/gadgets/src/signed_integer/arithmetic/twos_complement.rs
new file mode 100644
index 0000000000..171f36d843
--- /dev/null
+++ b/gadgets/src/signed_integer/arithmetic/twos_complement.rs
@@ -0,0 +1,58 @@
+use crate::{binary::RippleCarryAdder, errors::IntegerError, signed_integer::*};
+
+use snarkos_models::{curves::PrimeField, gadgets::r1cs::ConstraintSystem};
+
+/// Inverts the given number and adds 1 to the lsb of the result
+pub trait TwosComplement
+where
+    Self: std::marker::Sized,
+{
+    #[must_use]
+    fn twos_comp<F: PrimeField, CS: ConstraintSystem<F>>(&self, cs: CS) -> Result<Self, IntegerError>;
+}
+
+macro_rules! twos_comp_int_impl {
+    ($($gadget: ident)*) => ($(
+        impl TwosComplement for $gadget {
+            fn twos_comp<F: PrimeField, CS: ConstraintSystem<F>>(
+                &self,
+                mut cs: CS
+            ) -> Result<Self, IntegerError> {
+                let value = match self.value {
+                    Some(val) => {
+                        match val.checked_neg() {
+                            Some(val_neg) => Some(val_neg),
+                            None => return Err(IntegerError::NegativeZero) // -0 should fail
+                        }
+                    }
+                    None => None,
+                };
+                println!("val {}", value.unwrap());
+
+                // flip all bits
+                let flipped_bits = self.bits
+                    .iter()
+                    .map(|bit| bit.not())
+                    .collect();
+
+                let flipped = Self {
+                    bits: flipped_bits,
+                    value,
+                };
+
+                // add one
+                let one = Self::one();
+
+                let mut bits = flipped.add_bits(cs.ns(|| format!("add one")), &one)?;
+                let _carry = bits.pop(); // we already accounted for overflow above
+
+                Ok(Self {
+                    bits,
+                    value,
+                })
+            }
+        }
+    )*)
+}
+
+twos_comp_int_impl!(Int8 Int16 Int32 Int64 Int128);
diff --git a/gadgets/src/signed_integer/int_impl.rs b/gadgets/src/signed_integer/int_impl.rs
index b5a3e7fd82..b61fde07a6 100644
--- a/gadgets/src/signed_integer/int_impl.rs
+++ b/gadgets/src/signed_integer/int_impl.rs
@@ -6,6 +6,8 @@ pub trait Int: Debug + Clone {
     type IntegerType;
     const SIZE: usize;
 
+    fn one() -> Self;
+
     /// Returns true if all bits in this `Int` are constant
     fn is_constant(&self) -> bool;
 
@@ -13,8 +15,6 @@ pub trait Int: Debug + Clone {
     fn result_is_constant(first: &Self, second: &Self) -> bool {
         first.is_constant() && second.is_constant()
     }
-
-    fn is_negative(&self) -> bool;
 }
 
 /// Implements the base struct for a signed integer gadget
@@ -55,6 +55,10 @@ macro_rules! int_impl {
 
             const SIZE: usize = $size;
 
+            fn one() -> Self {
+                Self::constant(1 as $type_)
+            }
+
             fn is_constant(&self) -> bool {
                 let mut constant = true;
 
@@ -69,10 +73,6 @@ macro_rules! int_impl {
 
                 constant
             }
-
-            fn is_negative(&self) -> bool {
-                true
-            }
         }
     };
 }
diff --git a/gadgets/tests/signed_integer/i8.rs b/gadgets/tests/signed_integer/i8.rs
index 6271cca340..468bf91e90 100644
--- a/gadgets/tests/signed_integer/i8.rs
+++ b/gadgets/tests/signed_integer/i8.rs
@@ -1,4 +1,7 @@
-use leo_gadgets::{arithmetic::Add, Int8};
+use leo_gadgets::{
+    arithmetic::{Add, Neg},
+    Int8,
+};
 use snarkos_models::{
     curves::{One, Zero},
     gadgets::{
@@ -102,3 +105,29 @@ fn test_int8_add() {
         assert!(!cs.is_satisfied());
     }
 }
+
+#[test]
+fn test_int8_neg_constants() {
+    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+
+    for _ in 0..1 {
+        let a: i8 = rng.gen();
+
+        println!("{}", a);
+
+        let a_bit = Int8::constant(a);
+
+        let r = a_bit.neg();
+
+        match a.checked_neg() {
+            Some(expected) => {
+                println!("result {}", expected);
+                let result = r.unwrap();
+                assert!(result.value == Some(expected));
+
+                check_all_constant_bits(expected, result);
+            }
+            None => assert!(r.is_none()),
+        }
+    }
+}