diff --git a/brillig_bytecode/src/lib.rs b/brillig_bytecode/src/lib.rs
index 1c3267cef..70f5b6673 100644
--- a/brillig_bytecode/src/lib.rs
+++ b/brillig_bytecode/src/lib.rs
@@ -170,7 +170,7 @@ fn test_jmpif_opcode() {
 
     let equal_cmp_opcode = Opcode::BinaryOp {
         result_type: Typ::Field,
-        op: BinaryOp::Cmp(Comparison::Equal),
+        op: BinaryOp::Cmp(Comparison::Eq),
         lhs: RegisterMemIndex::Register(RegisterIndex(0)),
         rhs: RegisterMemIndex::Register(RegisterIndex(1)),
         result: RegisterIndex(2),
@@ -207,7 +207,7 @@ fn test_jmpifnot_opcode() {
 
     let not_equal_cmp_opcode = Opcode::BinaryOp {
         result_type: Typ::Field,
-        op: BinaryOp::Cmp(Comparison::Equal),
+        op: BinaryOp::Cmp(Comparison::Eq),
         lhs: RegisterMemIndex::Register(RegisterIndex(0)),
         rhs: RegisterMemIndex::Register(RegisterIndex(1)),
         result: RegisterIndex(2),
@@ -277,3 +277,77 @@ fn test_mov_opcode() {
     let source_value = registers.get(RegisterMemIndex::Register(RegisterIndex(0)));
     assert_eq!(source_value, Value::from(1u128));
 }
+
+#[test]
+fn test_cmp_binary_ops() {
+    let input_registers = Registers::load(vec![
+        Value::from(2u128),
+        Value::from(2u128),
+        Value::from(0u128),
+        Value::from(5u128),
+        Value::from(6u128),
+    ]);
+
+    let equal_opcode = Opcode::BinaryOp {
+        result_type: Typ::Field,
+        op: BinaryOp::Cmp(Comparison::Eq),
+        lhs: RegisterMemIndex::Register(RegisterIndex(0)),
+        rhs: RegisterMemIndex::Register(RegisterIndex(1)),
+        result: RegisterIndex(2),
+    };
+
+    let not_equal_opcode = Opcode::BinaryOp {
+        result_type: Typ::Field,
+        op: BinaryOp::Cmp(Comparison::Eq),
+        lhs: RegisterMemIndex::Register(RegisterIndex(0)),
+        rhs: RegisterMemIndex::Register(RegisterIndex(3)),
+        result: RegisterIndex(2),
+    };
+
+    let less_than_opcode = Opcode::BinaryOp {
+        result_type: Typ::Field,
+        op: BinaryOp::Cmp(Comparison::Lt),
+        lhs: RegisterMemIndex::Register(RegisterIndex(3)),
+        rhs: RegisterMemIndex::Register(RegisterIndex(4)),
+        result: RegisterIndex(2),
+    };
+
+    let less_than_equal_opcode = Opcode::BinaryOp {
+        result_type: Typ::Field,
+        op: BinaryOp::Cmp(Comparison::Lte),
+        lhs: RegisterMemIndex::Register(RegisterIndex(3)),
+        rhs: RegisterMemIndex::Register(RegisterIndex(4)),
+        result: RegisterIndex(2),
+    };
+
+    let mut vm = VM::new(
+        input_registers,
+        vec![equal_opcode, not_equal_opcode, less_than_opcode, less_than_equal_opcode],
+    );
+
+    let status = vm.process_opcode();
+    assert_eq!(status, VMStatus::InProgress);
+
+    let output_eq_value = vm.registers.get(RegisterMemIndex::Register(RegisterIndex(2)));
+    assert_eq!(output_eq_value, Value::from(true));
+
+    let status = vm.process_opcode();
+    assert_eq!(status, VMStatus::InProgress);
+
+    let output_neq_value = vm.registers.get(RegisterMemIndex::Register(RegisterIndex(2)));
+    assert_eq!(output_neq_value, Value::from(false));
+
+    let status = vm.process_opcode();
+    assert_eq!(status, VMStatus::InProgress);
+
+    let lt_value = vm.registers.get(RegisterMemIndex::Register(RegisterIndex(2)));
+    assert_eq!(lt_value, Value::from(true));
+
+    let status = vm.process_opcode();
+    assert_eq!(status, VMStatus::Halted);
+
+    let lte_value = vm.registers.get(RegisterMemIndex::Register(RegisterIndex(2)));
+    assert_eq!(lte_value, Value::from(true));
+
+    vm.finish();
+}
diff --git a/brillig_bytecode/src/opcodes.rs b/brillig_bytecode/src/opcodes.rs
index e8e054401..fca46f4ee 100644
--- a/brillig_bytecode/src/opcodes.rs
+++ b/brillig_bytecode/src/opcodes.rs
@@ -79,8 +79,9 @@ pub enum BinaryOp {
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
 pub enum Comparison {
-    NotEqual,
-    Equal,
+    Eq,  //(==) equal
+    Lt,  //(<) field less
+    Lte, //(<=) field less or equal
 }
 
 impl BinaryOp {
@@ -90,8 +91,11 @@ impl BinaryOp {
             BinaryOp::Sub => |a: Value, b: Value| a - b,
             BinaryOp::Mul => |a: Value, b: Value| a * b,
             BinaryOp::Div => |a: Value, b: Value| a / b,
-            // TODO: only support equal and not equal, need less than, greater than, etc.
-            BinaryOp::Cmp(_) => |a: Value, b: Value| (a == b).into(),
+            BinaryOp::Cmp(comparison) => match comparison {
+                Comparison::Eq => |a: Value, b: Value| (a == b).into(),
+                Comparison::Lt => |a: Value, b: Value| (a.inner < b.inner).into(),
+                Comparison::Lte => |a: Value, b: Value| (a.inner <= b.inner).into(),
+            },
         }
     }
 }
diff --git a/brillig_bytecode/src/value.rs b/brillig_bytecode/src/value.rs
index 84484dd86..d5bd3d9fb 100644
--- a/brillig_bytecode/src/value.rs
+++ b/brillig_bytecode/src/value.rs
@@ -3,7 +3,7 @@ use serde::{Deserialize, Serialize};
 use std::ops::{Add, Div, Mul, Neg, Sub};
 
 /// Types of values allowed in the VM
-#[derive(Debug, Copy, Clone, PartialEq, Eq, Serialize, Deserialize)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Serialize, Deserialize, PartialOrd, Ord)]
 pub enum Typ {
     Field,
     Unsigned { bit_size: u32 },
@@ -11,7 +11,7 @@ pub enum Typ {
 }
 
 /// Value represents a Value in the VM
-#[derive(Debug, Copy, Clone, PartialEq, Eq)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
 pub struct Value {
     pub typ: Typ,
     pub inner: FieldElement,