Another way to compare the contents of two files at the byte level is to hash both of them and compare the hashes. (it's the entire purpose of digest hashes).

$ dd if=/dev/urandom of=file1 bs=1K count=10
10+0 records in
10+0 records out
10240 bytes (10 kB, 10 KiB) copied, 0.000148608 s, 68.9 MB/s
$ dd if=/dev/urandom of=file2 bs=1K count=10
10+0 records in
10+0 records out
10240 bytes (10 kB, 10 KiB) copied, 0.000145675 s, 70.3 MB/s
$ ls -l
total 24
-rw-r--r-- 1 foo foo 10240 Feb  9 17:47 file1
-rw-r--r-- 1 foo foo 10240 Feb  9 17:47 file2
$ sha256sum *
7986a677d3ef9a4f71ba18a5a7bd3a5f9a0c2d16939b4a43cd49fde86cef5a2f  file
+1
3c946e3212d808dbb7471eecc07e454c459352a6a3e25230288fe5faf08af555  file
+2
[download]

This shows that despite file1 and file2 having precisely the same size, their contents differ because the SHA256 hashes differ. See sha256sum for more.

See sha256sum for more.

Or use the standard perl utility: shasum -h