diff --git a/src/ast.rs b/src/ast.rs
index 8ea0d02..a509cab 100644
--- a/src/ast.rs
+++ b/src/ast.rs
@@ -69,9 +69,9 @@ impl fmt::Debug for NumLitStr {
 /// before and after any digit.
 #[derive(Clone)]
 pub struct NumLit {
-    value: i64,
-    str: NumLitStr,
-    span: Span,
+    pub value: i64,
+    pub str: NumLitStr,
+    pub span: Span,
 }
 
 impl fmt::Debug for NumLit {
diff --git a/src/parser.rs b/src/parser.rs
index f1e5b26..727d059 100644
--- a/src/parser.rs
+++ b/src/parser.rs
@@ -1,10 +1,14 @@
 use chumsky::prelude::*;
+use chumsky::text::Character;
 
-use crate::ast::{Ident, Space};
+use crate::ast::{Ident, NumLit, NumLitStr, Space};
 use crate::span::Span;
 
 type Error = Simple<char, Span>;
 
+// This would probably look a lot nicer with type_alias_impl_trait:
+// https://github.com/rust-lang/rust/issues/63063
+
 fn space() -> impl Parser<char, Space, Error = Error> {
     // TODO Parse comments
     text::whitespace().map_with_span(|(), span| Space {
@@ -17,6 +21,63 @@ fn ident() -> impl Parser<char, Ident, Error = Error> {
     text::ident().map_with_span(|name, span| Ident { name, span })
 }
 
-pub fn parser() -> impl Parser<char, Ident, Error = Error> {
-    ident().padded().then_ignore(end())
+fn num_lit_str_radix(radix: u32) -> impl Parser<char, (i64, NumLitStr), Error = Error> {
+    // Minimum amount of digits required to represent i64::MAX. The rest of this
+    // code assumes that any value that can be represented using this amount of
+    // digits fits into an u64.
+    let max_digits = match radix {
+        2 => 63,
+        10 => 19,
+        16 => 16,
+        _ => panic!("unsupported radix"),
+    };
+
+    // Representations of i64::MAX.
+    let max_value = match radix {
+        2 => "0b_1111111_11111111_11111111_11111111_11111111_11111111_11111111_11111111",
+        10 => "9_223_372_036_854_775_807",
+        16 => "0x_7fff_ffff_ffff_ffff",
+        _ => panic!("unsupported radix"),
+    };
+
+    let constructor = match radix {
+        2 => NumLitStr::Bin,
+        10 => NumLitStr::Dec,
+        16 => NumLitStr::Hex,
+        _ => panic!("unsupported radix"),
+    };
+
+    filter(move |c: &char| c.is_digit(radix) || *c == '_')
+        .repeated()
+        .at_least(1)
+        .collect::<String>()
+        .try_map(move |s, span| {
+            let digits = s.chars().filter(|c| *c != '_').collect::<String>();
+            if digits.is_empty() {
+                let msg = "integer literal needs to contain at least one digit";
+                return Err(Simple::custom(span, msg));
+            } else if digits.len() > max_digits {
+                let msg = format!("integer literal too large, the maximum value is {max_value}");
+                return Err(Simple::custom(span, msg));
+            }
+
+            let value = u64::from_str_radix(&digits, radix).unwrap();
+            if value <= i64::MAX as u64 {
+                Ok((value as i64, constructor(s)))
+            } else {
+                let msg = format!("integer literal too large, the maximum value is {max_value}");
+                Err(Simple::custom(span, msg))
+            }
+        })
+}
+
+fn num_lit() -> impl Parser<char, NumLit, Error = Error> {
+    (just("0b").ignore_then(num_lit_str_radix(2)))
+        .or(just("0x").ignore_then(num_lit_str_radix(16)))
+        .or(num_lit_str_radix(10))
+        .map_with_span(|(value, str), span| NumLit { value, str, span })
+}
+
+pub fn parser() -> impl Parser<char, NumLit, Error = Error> {
+    num_lit().padded().then_ignore(end())
 }