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10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                                                    Number
                                                    Systems
                                                        An Introduction




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                                                             Goal

                           To appreciate the importance of
                       binary and hexadecimal number systems
                               in the computer world.




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer


                                                                                                                               H Building
                                                                                                                                Switch




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                                                               H Building
                                                                                                                                Switch




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                                                               H Building
                                                                                                                                Switch

                                                                                                       C Building
                                                                                                        Router




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                                                                                (Bell)




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                                                                                (Bell)
                                                            Chicago




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                                                                                (Bell)
                                                            Chicago
                                       Los Angeles




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                        that’s through                                                 C Building
                                      undersea cables in                                                Router
                                      the Pacific Ocean                         Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch            Ateneo
                             www
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch            Ateneo
                             www
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router                                               All the “conversations” done in
         Ateneo
                                                                      a matter of seconds.
       server room
          switch            Ateneo
                                                                   With data travelling at the
                             www
                            server
                                                                         speed of light.
 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                               Request
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch            Ateneo
                             www
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch          Ateneo
                         Request
                            www
                           server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch          Ateneo
                         Response
                            www
                           server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                              Response
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router


         Ateneo
       server room
          switch            Ateneo
                             www
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                                Rowntree
                                                                                                                              Response
                                                                                                                                Theater
                                                                                                                               computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router
                                                               “Conversations” are encoded
         Ateneo
       server room
                                                             as digital signals (binary) for travel
          switch            Ateneo
                             www
                                                              across wires and through the air.
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                               Rowntree
                                                                                                                             10110100
                                                                                                                               Theater
                                                                                                                              computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router
                                                                And what’s amazing is that
         Ateneo
       server room
                                                                data reaches us intact and
          switch            Ateneo
                             www
                                                            with no errors (most of the time).
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                       Let’s take a little trip                                                                               Rowntree
                                                                                                                             11101011
                                                                                                                               Theater
                                                                                                                              computer
                                                                                                           C Building
                                                                                                            Switch
                                                                                       Barrie                                  H Building
                                                                                       (Bell)                                   Switch

                                                                                                       C Building
                                                                                                        Router
                                                                               Toronto
                      Manila                                                    (Bell)
                                                            Chicago
                                       Los Angeles
       Ateneo
      main router
                                                                And what’s amazing is that
         Ateneo
       server room
                                                                data reaches us intact and
          switch            Ateneo
                             www
                                                            with no errors (most of the time).
                            server


 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




         Pictures are stored as bits




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




               Songs are stored as bits




 MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001




                                   Binary, Decimal,
                                    Hexadecimal

                         Binary is the language of the computer.
                         Decimal is the human number system.
                         Hexadecimal is used to bridge the two.




 MATH1003

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