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The first binary encoding of alphanumeric characters was indeed designed nearly a century ago , by Giuseppe Peano , the very Peano responsible for the first axiomatization of arithmetics . These include the concept of electronic digital computation , the use of a binary system of arithmetic , separation of computing and memory functions , regenerative drum memory , use of electronic amplifiers as on-off switches , circuits for logical addition and subtraction , clocked control of electronic operation and modular design construction . In the following axioms , AtomSentPA ( A ) expresses that A is an atomic sentence of the language of arithmetic , SentPA ( A ) expresses that A is a sentence of the language of arithmetic . The package provides support for several extended precision arithmetics , including user-defined types . " We now know that very young children can understand and solve problems involving simple multiplication and division well before they have the maturity to learn all their arithmetic facts . An analysis of numerical algorithms gives important suggestions for better implementing machine arithmetics ; algorithms analysis is itself a source for suggesting various possible redefinitions of computer structure . This nanoprocessor should be programmable and reprogrammable , and it should perform logic functions including arithmetics . Instead of seeing math as a beautiful system in which arithmetic , algebra and geometry all worked together to allow one to solve problems , they saw it as a bunch of jumbled rules which made little sense that they were forced to memorize . So one could only gain one indirection ( the arithmetics is more or less free , as it can be done in parallel ) .