diff --git a/src/uu/hashsum/src/digest.rs b/src/uu/hashsum/src/digest.rs
index 531dc7e4f..61f425662 100644
--- a/src/uu/hashsum/src/digest.rs
+++ b/src/uu/hashsum/src/digest.rs
@@ -189,13 +189,31 @@ pub struct DigestWriter<'a> {
     /// "\n" before passing input bytes to the [`digest`].
     #[allow(dead_code)]
     binary: bool,
-    // TODO This is dead code only on non-Windows operating systems. It
-    // might be better to use a `#[cfg(windows)]` guard here.
+
+    /// Whether the previous
+    #[allow(dead_code)]
+    was_last_character_carriage_return: bool,
+    // TODO These are dead code only on non-Windows operating systems.
+    // It might be better to use a `#[cfg(windows)]` guard here.
 }
 
 impl<'a> DigestWriter<'a> {
     pub fn new(digest: &'a mut Box<dyn Digest>, binary: bool) -> DigestWriter {
-        DigestWriter { digest, binary }
+        let was_last_character_carriage_return = false;
+        DigestWriter {
+            digest,
+            binary,
+            was_last_character_carriage_return,
+        }
+    }
+
+    pub fn finalize(&mut self) -> bool {
+        if self.was_last_character_carriage_return {
+            self.digest.input(&[b'\r']);
+            true
+        } else {
+            false
+        }
     }
 }
 
@@ -213,22 +231,40 @@ impl<'a> Write for DigestWriter<'a> {
             return Ok(buf.len());
         }
 
-        // In Windows text mode, replace each occurrence of "\r\n"
-        // with "\n".
+        // The remaining code handles Windows text mode, where we must
+        // replace each occurrence of "\r\n" with "\n".
         //
-        // Find all occurrences of "\r\n", inputting the slice just
-        // before the "\n" in the previous instance of "\r\n" and
-        // the beginning of this "\r\n".
-        //
-        // FIXME This fails if one call to `write()` ends with the
-        // "\r" and the next call to `write()` begins with the "\n".
+        // First, if the last character written was "\r" and the first
+        // character in the current buffer to write is not "\n", then we
+        // need to write the "\r" that we buffered from the previous
+        // call to `write()`.
         let n = buf.len();
+        if self.was_last_character_carriage_return && n > 0 && buf[0] != b'\n' {
+            self.digest.input(&[b'\r']);
+        }
+
+        // Next, find all occurrences of "\r\n", inputting the slice
+        // just before the "\n" in the previous instance of "\r\n" and
+        // the beginning of this "\r\n".
         let mut i_prev = 0;
         for i in memmem::find_iter(buf, b"\r\n") {
             self.digest.input(&buf[i_prev..i]);
             i_prev = i + 1;
         }
-        self.digest.input(&buf[i_prev..n]);
+
+        // Finally, check whether the last character is "\r". If so,
+        // buffer it until we know that the next character is not "\n",
+        // which can only be known on the next call to `write()`.
+        //
+        // This all assumes that `write()` will be called on adjacent
+        // blocks of the input.
+        if n > 0 && buf[n - 1] == b'\r' {
+            self.was_last_character_carriage_return = true;
+            self.digest.input(&buf[i_prev..n - 1]);
+        } else {
+            self.was_last_character_carriage_return = false;
+            self.digest.input(&buf[i_prev..n]);
+        }
 
         // Even though we dropped a "\r" for each "\r\n" we found, we
         // still report the number of bytes written as `n`. This is
@@ -243,3 +279,36 @@ impl<'a> Write for DigestWriter<'a> {
         Ok(())
     }
 }
+
+#[cfg(test)]
+mod tests {
+
+    /// Test for replacing a "\r\n" sequence with "\n" when the "\r" is
+    /// at the end of one block and the "\n" is at the beginning of the
+    /// next block, when reading in blocks.
+    #[cfg(windows)]
+    #[test]
+    fn test_crlf_across_blocks() {
+        use std::io::Write;
+
+        use crate::digest::Digest;
+        use crate::digest::DigestWriter;
+
+        // Writing "\r" in one call to `write()`, and then "\n" in another.
+        let mut digest = Box::new(md5::Context::new()) as Box<dyn Digest>;
+        let mut writer_crlf = DigestWriter::new(&mut digest, false);
+        writer_crlf.write_all(&[b'\r']).unwrap();
+        writer_crlf.write_all(&[b'\n']).unwrap();
+        writer_crlf.finalize();
+        let result_crlf = digest.result_str();
+
+        // We expect "\r\n" to be replaced with "\n" in text mode on Windows.
+        let mut digest = Box::new(md5::Context::new()) as Box<dyn Digest>;
+        let mut writer_lf = DigestWriter::new(&mut digest, false);
+        writer_lf.write_all(&[b'\n']).unwrap();
+        writer_lf.finalize();
+        let result_lf = digest.result_str();
+
+        assert_eq!(result_crlf, result_lf);
+    }
+}
diff --git a/src/uu/hashsum/src/hashsum.rs b/src/uu/hashsum/src/hashsum.rs
index 4186043f5..07070ed1b 100644
--- a/src/uu/hashsum/src/hashsum.rs
+++ b/src/uu/hashsum/src/hashsum.rs
@@ -611,8 +611,16 @@ fn digest_reader<T: Read>(
     // If `binary` is `false` and the operating system is Windows, then
     // `DigestWriter` replaces "\r\n" with "\n" before it writes the
     // bytes into `digest`. Otherwise, it just inserts the bytes as-is.
+    //
+    // In order to support replacing "\r\n", we must call `finalize()`
+    // in order to support the possibility that the last character read
+    // from the reader was "\r". (This character gets buffered by
+    // `DigestWriter` and only written if the following character is
+    // "\n". But when "\r" is the last character read, we need to force
+    // it to be written.)
     let mut digest_writer = DigestWriter::new(digest, binary);
     std::io::copy(reader, &mut digest_writer)?;
+    digest_writer.finalize();
 
     if digest.output_bits() > 0 {
         Ok(digest.result_str())