diff --git a/src/dtype.rs b/src/dtype.rs
index b21aa208..a2c92aa7 100644
--- a/src/dtype.rs
+++ b/src/dtype.rs
@@ -1,4 +1,4 @@
-use crate::CpuStorage;
+use crate::{CpuStorage, Error, Result};
 
 #[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
 pub enum DType {
@@ -19,6 +19,8 @@ pub trait WithDType: Sized + Copy {
     const DTYPE: DType;
 
     fn to_cpu_storage(data: &[Self]) -> CpuStorage;
+
+    fn cpu_storage_as_slice(s: &CpuStorage) -> Result<&[Self]>;
 }
 
 impl WithDType for f32 {
@@ -27,6 +29,16 @@ impl WithDType for f32 {
     fn to_cpu_storage(data: &[Self]) -> CpuStorage {
         CpuStorage::F32(data.to_vec())
     }
+
+    fn cpu_storage_as_slice(s: &CpuStorage) -> Result<&[Self]> {
+        match s {
+            CpuStorage::F32(data) => Ok(data),
+            _ => Err(Error::UnexpectedDType {
+                expected: DType::F32,
+                got: s.dtype(),
+            }),
+        }
+    }
 }
 
 impl WithDType for f64 {
@@ -35,4 +47,14 @@ impl WithDType for f64 {
     fn to_cpu_storage(data: &[Self]) -> CpuStorage {
         CpuStorage::F64(data.to_vec())
     }
+
+    fn cpu_storage_as_slice(s: &CpuStorage) -> Result<&[Self]> {
+        match s {
+            CpuStorage::F64(data) => Ok(data),
+            _ => Err(Error::UnexpectedDType {
+                expected: DType::F64,
+                got: s.dtype(),
+            }),
+        }
+    }
 }
diff --git a/src/error.rs b/src/error.rs
index 12386268..7416ed76 100644
--- a/src/error.rs
+++ b/src/error.rs
@@ -1,10 +1,15 @@
+use crate::{DType, Shape};
+
 /// Main library error type.
 #[derive(thiserror::Error, Debug)]
 pub enum Error {
-    #[error("invalid shapes in {op}, lhs: {lhs:?}, rhs: {rhs:?}")]
-    BinaryInvalidShape {
-        lhs: Vec<usize>,
-        rhs: Vec<usize>,
+    #[error("unexpected dtype, expected: {expected:?}, got: {got:?}")]
+    UnexpectedDType { expected: DType, got: DType },
+
+    #[error("shape mismatch in {op}, lhs: {lhs:?}, rhs: {rhs:?}")]
+    ShapeMismatchBinaryOp {
+        lhs: Shape,
+        rhs: Shape,
         op: &'static str,
     },
 
@@ -12,7 +17,7 @@ pub enum Error {
     UnexpectedNumberOfDims {
         expected: usize,
         got: usize,
-        shape: Vec<usize>,
+        shape: Shape,
     },
 }
 
diff --git a/src/shape.rs b/src/shape.rs
index a5fee614..4b186ca0 100644
--- a/src/shape.rs
+++ b/src/shape.rs
@@ -1,4 +1,6 @@
 use crate::{Error, Result};
+
+#[derive(Clone, PartialEq, Eq)]
 pub struct Shape(pub(crate) Vec<usize>);
 
 impl std::fmt::Debug for Shape {
@@ -56,6 +58,10 @@ impl From<(usize, usize, usize)> for Shape {
 }
 
 impl Shape {
+    pub fn from_dims(dims: &[usize]) -> Self {
+        Self(dims.to_vec())
+    }
+
     pub fn rank(&self) -> usize {
         self.0.len()
     }
@@ -76,7 +82,7 @@ impl Shape {
             Err(Error::UnexpectedNumberOfDims {
                 expected: 0,
                 got: shape.len(),
-                shape: shape.to_vec(),
+                shape: self.clone(),
             })
         }
     }
@@ -89,7 +95,7 @@ impl Shape {
             Err(Error::UnexpectedNumberOfDims {
                 expected: 1,
                 got: shape.len(),
-                shape: shape.to_vec(),
+                shape: self.clone(),
             })
         }
     }
@@ -102,7 +108,7 @@ impl Shape {
             Err(Error::UnexpectedNumberOfDims {
                 expected: 2,
                 got: shape.len(),
-                shape: shape.to_vec(),
+                shape: self.clone(),
             })
         }
     }
@@ -115,7 +121,7 @@ impl Shape {
             Err(Error::UnexpectedNumberOfDims {
                 expected: 3,
                 got: shape.len(),
-                shape: shape.to_vec(),
+                shape: self.clone(),
             })
         }
     }
@@ -128,7 +134,7 @@ impl Shape {
             Err(Error::UnexpectedNumberOfDims {
                 expected: 4,
                 got: shape.len(),
-                shape: shape.to_vec(),
+                shape: self.clone(),
             })
         }
     }
diff --git a/src/tensor.rs b/src/tensor.rs
index 9b1e7d5b..83aa00d7 100644
--- a/src/tensor.rs
+++ b/src/tensor.rs
@@ -1,4 +1,4 @@
-use crate::{op::Op, storage::Storage, DType, Device, Result, Shape};
+use crate::{op::Op, storage::Storage, DType, Device, Error, Result, Shape};
 use std::sync::Arc;
 
 #[allow(dead_code)]
@@ -45,11 +45,46 @@ impl Tensor {
         Ok(Self(Arc::new(tensor_)))
     }
 
-    pub fn to_scalar<S: crate::WithDType>(&self) -> Result<S> {
-        // TODO: properly use the strides here.
+    pub(crate) fn same_shape_binary_op(&self, rhs: &Self, op: &'static str) -> Result<()> {
+        let lhs = self.shape();
+        let rhs = rhs.shape();
+        if lhs != rhs {
+            Err(Error::ShapeMismatchBinaryOp {
+                lhs: lhs.clone(),
+                rhs: rhs.clone(),
+                op,
+            })
+        } else {
+            Ok(())
+        }
+    }
+
+    pub fn add(&self, rhs: &Self) -> Result<Self> {
+        self.same_shape_binary_op(rhs, "add")?;
         todo!()
     }
 
+    pub fn mul(&self, rhs: &Self) -> Result<Self> {
+        self.same_shape_binary_op(rhs, "mul")?;
+        todo!()
+    }
+
+    pub fn to_scalar<S: crate::WithDType>(&self) -> Result<S> {
+        if self.rank() != 0 {
+            return Err(Error::UnexpectedNumberOfDims {
+                expected: 0,
+                got: self.rank(),
+                shape: self.shape().clone(),
+            });
+        }
+        match &self.0.storage {
+            Storage::Cpu(cpu_storage) => {
+                let data = S::cpu_storage_as_slice(cpu_storage)?;
+                Ok(data[0])
+            }
+        }
+    }
+
     pub fn to_vec1<S: crate::WithDType>(&self) -> Result<Vec<S>> {
         // TODO: properly use the strides here.
         todo!()
diff --git a/tests/tensor_tests.rs b/tests/tensor_tests.rs
index 54c1e987..a0f4630d 100644
--- a/tests/tensor_tests.rs
+++ b/tests/tensor_tests.rs
@@ -6,7 +6,7 @@ fn add() -> Result<()> {
     let (dim1, dim2) = tensor.shape().r2()?;
     assert_eq!(dim1, 5);
     assert_eq!(dim2, 2);
-    let tensor = Tensor::new([3., 1., 4.].as_slice(), Device::Cpu)?;
+    let tensor = Tensor::new([3f32, 1., 4.].as_slice(), Device::Cpu)?;
     let dim1 = tensor.shape().r1()?;
     assert_eq!(dim1, 3);
     Ok(())