Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel?

Gottfried Wilhelm Leibniz (1646-1716) is the self-proclaimed inventor of the binary system and is considered as such by most historians of mathematics and/or mathematicians. Really though, we owe the groundwork of today's computing not to Leibniz but to the Englishman Thomas Harriot and the Spaniard Juan Caramuel de Lobkowitz (1606-1682), whom Leibniz plagiarized. This plagiarism has been identified on the basis of several facts: Caramuel's work on the binary system is earlier than Leibniz's, Leibniz was acquainted-both directly and indirectly-with Caramuel's work and Leibniz had a natural tendency to plagiarize scientific works.