diff --git a/src/cpu/run/arithutil.rs b/src/cpu/run/arithutil.rs
index a760899..7c71f4a 100644
--- a/src/cpu/run/arithutil.rs
+++ b/src/cpu/run/arithutil.rs
@@ -1,6 +1,6 @@
 //! arithutil contains utilities to generalize the implementation of arithmetic instructions
 
-use std::{marker::PhantomData, ops::Add};
+use std::ops::Add;
 
 use thiserror::Error;
 
@@ -16,16 +16,15 @@ pub enum Error {
 /// `CarriedNumber` is a number combined with its carry bit, intended to be used to perform carry-based arithmetic
 /// operations such as ADC.
 #[derive(Debug, Clone, Copy, PartialEq)]
-pub struct CarriedNumber<N, V> {
+pub struct CarriedNumber<N> {
     num: N,
     carry_bit: u8,
-    _phantom: PhantomData<V>,
 }
 
-impl<N, V> CarriedNumber<N, V>
+impl<N> CarriedNumber<N>
 where
-    N: Copy + Clone + PartialEq + UpgradableNumber<V>,
-    V: From<N> + From<u8> + Add<Output = V>,
+    N: Copy + Clone + PartialEq + UpgradableNumber,
+    N::Output: From<u8> + Add<Output = N::Output>,
 {
     /// Create a new [`CarriedNumber`] with a raw value and its carry bit. Note that the carry bit must be 0 or 1,
     /// or an [`Error::InvalidCarryBit`] will be returned
@@ -34,17 +33,13 @@ where
             return Err(Error::InvalidCarryBit(carry_bit));
         }
 
-        Ok(Self {
-            num,
-            carry_bit,
-            _phantom: PhantomData,
-        })
+        Ok(Self { num, carry_bit })
     }
 
     /// Get the combination between the value and the carry bit. The return value is the "upgraded" version of `N`.
     /// See [`upgrade::UpgradableNumber`] for more details
-    pub fn value(self) -> V {
-        self.num.upgrade() + V::from(self.carry_bit)
+    pub fn value(self) -> N::Output {
+        self.num.upgrade() + self.carry_bit.into()
     }
 
     /// Get the number and its carry bit directly
@@ -116,8 +111,8 @@ impl CarryingAdd<i8, u16> for u16 {
     }
 }
 
-impl CarryingAdd<CarriedNumber<u8, u16>, u8> for u8 {
-    fn add_with_carry(self, rhs: CarriedNumber<u8, u16>) -> (u8, bool, bool) {
+impl CarryingAdd<CarriedNumber<u8>, u8> for u8 {
+    fn add_with_carry(self, rhs: CarriedNumber<u8>) -> (u8, bool, bool) {
         let total = rhs.value() + u16::from(self);
         // Given this is adding two u8s, the largest value we can produce is 0x01FF (both operands 0xFF, plus a carry bit)
         // which can never wrap, so we just take the lower byte to convert back to u8
@@ -140,8 +135,8 @@ impl CarryingSub<u8, u8> for u8 {
     }
 }
 
-impl CarryingSub<CarriedNumber<u8, u16>, u8> for u8 {
-    fn sub_with_carry(self, rhs: CarriedNumber<u8, u16>) -> (u8, bool, bool) {
+impl CarryingSub<CarriedNumber<u8>, u8> for u8 {
+    fn sub_with_carry(self, rhs: CarriedNumber<u8>) -> (u8, bool, bool) {
         let total = self.wrapping_sub(rhs.num).wrapping_sub(rhs.carry_bit);
         // let half_carry = did_8bit_sub_half_carry(self, rhs.value());
         let half_carry = did_8bit_sub_half_carry_including_carry_bit(self, rhs.num, rhs.carry_bit);
@@ -309,7 +304,7 @@ mod tests {
     #[test_case(0xFF, CarriedNumber::new(0xFF, 1).unwrap(), (0xFF, true, true))]
     fn test_add_carried_number_to_u8(
         value: u8,
-        carried_number: CarriedNumber<u8, u16>,
+        carried_number: CarriedNumber<u8>,
         expected: (u8, bool, bool),
     ) {
         assert_eq!(expected, value.add_with_carry(carried_number));
@@ -332,11 +327,7 @@ mod tests {
     #[test_case(0xAB, CarriedNumber::new(0x5F, 1).unwrap(), (0x4B, true, false); "half borrow with carry bit and wrap")]
     #[test_case(0x0F, CarriedNumber::new(0xF0, 0).unwrap(), (0x1F, false, true); "full borrow without carry bit")]
     #[test_case(0x0F, CarriedNumber::new(0xEE, 1).unwrap(), (0x20, false, true); "full borrow with carry bit")]
-    fn test_sub_u8_from_u8_with_carry(
-        lhs: u8,
-        rhs: CarriedNumber<u8, u16>,
-        expected: (u8, bool, bool),
-    ) {
+    fn test_sub_u8_from_u8_with_carry(lhs: u8, rhs: CarriedNumber<u8>, expected: (u8, bool, bool)) {
         assert_eq!(expected, lhs.sub_with_carry(rhs));
     }
 }
diff --git a/src/cpu/run/arithutil/upgrade.rs b/src/cpu/run/arithutil/upgrade.rs
index ae290f9..58eeba0 100644
--- a/src/cpu/run/arithutil/upgrade.rs
+++ b/src/cpu/run/arithutil/upgrade.rs
@@ -1,22 +1,37 @@
 /// `UpgradableNumber` represents an number that can be "upgraded" to its next largest type.
 /// This is slightly different than `From`, in that it only allows you to upgrade "one step up".
 /// You cannot, for instance, upgrade a `u8` to a `u64` directly.
-pub trait UpgradableNumber<U: From<Self>>
+pub trait UpgradableNumber
 where
     Self: Sized,
 {
-    fn upgrade(self) -> U {
+    type Output: From<Self>;
+
+    fn upgrade(self) -> Self::Output {
         self.into()
     }
 }
 
-impl UpgradableNumber<u16> for u8 {}
-impl UpgradableNumber<u32> for u16 {}
-impl UpgradableNumber<u64> for u32 {}
+impl UpgradableNumber for u8 {
+    type Output = u16;
+}
+impl UpgradableNumber for u16 {
+    type Output = u32;
+}
+impl UpgradableNumber for u32 {
+    type Output = u64;
+}
 
-impl UpgradableNumber<i16> for i8 {}
-impl UpgradableNumber<i32> for i16 {}
-impl UpgradableNumber<i64> for i32 {}
+impl UpgradableNumber for i8 {
+    type Output = i16;
+}
+impl UpgradableNumber for i16 {
+    type Output = i32;
+}
+
+impl UpgradableNumber for i32 {
+    type Output = i64;
+}
 
 #[cfg(test)]
 mod tests {