{ "patcher" : { "fileversion" : 1, "appversion" : { "major" : 6, "minor" : 0, "revision" : 8 } , "rect" : [ 918.0, 223.0, 838.0, 588.0 ], "bglocked" : 0, "openinpresentation" : 0, "default_fontsize" : 12.0, "default_fontface" : 0, "default_fontname" : "Arial", "gridonopen" : 0, "gridsize" : [ 15.0, 15.0 ], "gridsnaponopen" : 0, "statusbarvisible" : 2, "toolbarvisible" : 1, "boxanimatetime" : 200, "imprint" : 0, "enablehscroll" : 1, "enablevscroll" : 1, "devicewidth" : 0.0, "description" : "", "digest" : "", "tags" : "", "boxes" : [ { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-87", "linecount" : 3, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 585.0, 405.0, 225.0, 47.0 ], "text" : "Logical operators are sometimes called 'gates', especially in the context of electronics" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-85", "linecount" : 6, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 585.0, 465.0, 225.0, 87.0 ], "text" : "Look at the Wikipedia entry for \"XOR gate\" and see if you can write a Max patch that uses only NAND operators to make a XOR operator. It will be easier if you bundle the NAND code into a sub patch and make multiple copies of it." } } , { "box" : { "fontface" : 2, "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-80", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 675.0, 165.0, 45.0, 20.0 ], "presentation_rect" : [ 679.0, 165.0, 0.0, 0.0 ], "text" : "OR" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-81", "linecount" : 5, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 675.0, 195.0, 75.0, 74.0 ], "presentation_rect" : [ 679.0, 195.0, 0.0, 0.0 ], "text" : "In1 In2 Out\n0 0 0\n0 1 1\n1 0 1\n1 1 1" } } , { "box" : { "fontface" : 2, "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-79", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 585.0, 165.0, 45.0, 20.0 ], "text" : "AND" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-77", "linecount" : 5, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 585.0, 195.0, 75.0, 74.0 ], "text" : "In1 In2 Out\n0 0 0\n0 1 0\n1 0 0\n1 1 1" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-75", "linecount" : 4, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 585.0, 90.0, 225.0, 60.0 ], "text" : "A 'truth table' for a binary operator shows you what the output will be for all possible inputs. Here are the truth tables for AND and OR" } } , { "box" : { "id" : "obj-73", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 387.5, 525.0, 20.0, 20.0 ], "presentation_rect" : [ 409.5, 521.0, 0.0, 0.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-72", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 387.5, 465.0, 32.5, 20.0 ], "text" : "% 2" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-68", "maxclass" : "newobj", "numinlets" : 1, "numoutlets" : 2, "outlettype" : [ "bang", "int" ], "patching_rect" : [ 417.5, 405.0, 32.5, 20.0 ], "presentation_rect" : [ 436.5, 408.0, 0.0, 0.0 ], "text" : "t b i" } } , { "box" : { "id" : "obj-69", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 417.5, 375.0, 20.0, 20.0 ], "presentation_rect" : [ 436.5, 378.0, 0.0, 0.0 ] } } , { "box" : { "id" : "obj-70", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 387.5, 375.0, 20.0, 20.0 ], "presentation_rect" : [ 406.5, 378.0, 0.0, 0.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-71", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 387.5, 435.0, 32.5, 20.0 ], "text" : "+" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-66", "linecount" : 7, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 585.0, 285.0, 225.0, 100.0 ], "text" : "There are 16 possible binary operators. Some of them are \"universal\", in the sense that you can build all of the possible operators by using multiple copies of one of them. Both NAND and NOR operators are universal in this sense" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-64", "linecount" : 9, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 462.5, 375.0, 90.0, 127.0 ], "presentation_rect" : [ 542.0, 373.0, 0.0, 0.0 ], "text" : "The XOR (exclusive OR) operator returns 1 if its inputs are different, and returns 0 if they are the same" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-63", "linecount" : 8, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 293.75, 375.0, 81.25, 114.0 ], "presentation_rect" : [ 296.0, 378.0, 0.0, 0.0 ], "text" : "The NOR (NOT OR) operator returns 1 if its inputs are both 0, and returns 0 otherwise" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-56", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 216.25, 465.0, 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"parameter_enable" : 0, "patching_rect" : [ 180.0, 300.0, 20.0, 20.0 ], "presentation_rect" : [ 184.0, 296.0, 0.0, 0.0 ] } } , { "box" : { "id" : "obj-53", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 210.0, 195.0, 20.0, 20.0 ], "presentation_rect" : [ 214.0, 191.0, 0.0, 0.0 ] } } , { "box" : { "id" : "obj-54", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 180.0, 195.0, 20.0, 20.0 ], "presentation_rect" : [ 184.0, 191.0, 0.0, 0.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-55", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 180.0, 270.0, 32.5, 20.0 ], "text" : "&&" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-50", "linecount" : 7, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 105.0, 375.0, 90.0, 100.0 ], "text" : "The NAND (NOT AND) operator returns 0 if its inputs are both 1, and returns 1 otherwise" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-46", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 30.0, 465.0, 32.5, 20.0 ], "presentation_rect" : [ 147.0, 494.0, 0.0, 0.0 ], "text" : "- 1" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-47", "maxclass" : "newobj", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 30.0, 495.0, 30.0, 20.0 ], "presentation_rect" : [ 147.0, 524.0, 0.0, 0.0 ], "text" : "abs" } } , { "box" : { "id" : "obj-48", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 30.0, 525.0, 20.0, 20.0 ], "presentation_rect" : [ 147.0, 554.0, 0.0, 0.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-43", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 30.0, 345.0, 525.0, 20.0 ], "text" : "From these three logical operators we can build many others. Here are some examples..." } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-41", "linecount" : 5, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 450.0, 195.0, 105.0, 74.0 ], "text" : "The logical OR operator returns 0 if both of its inputs are 0, and returns 1 otherwise" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-39", "linecount" : 5, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 255.0, 195.0, 105.0, 74.0 ], "text" : "The logical AND operator returns 1 if both of its inputs are 1, and returns 0 otherwise" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-37", "linecount" : 3, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 30.0, 135.0, 210.0, 47.0 ], "text" : "Something that has two possible states is called a 'bit' (which is shorthand for 'binary digit')" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-35", "linecount" : 5, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 75.0, 195.0, 90.0, 74.0 ], "text" : "The logical NOT operator flips a bit from 0 to 1, or vice versa" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-33", "linecount" : 2, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 255.0, 135.0, 300.0, 33.0 ], "text" : "We use toggles to represent two possible states: unchecked / off / 0 versus checked / on / 1" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-29", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 30.0, 225.0, 32.5, 20.0 ], "text" : "- 1" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-28", "maxclass" : "newobj", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 30.0, 255.0, 30.0, 20.0 ], "text" : "abs" } } , { "box" : { "id" : "obj-27", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 30.0, 285.0, 20.0, 20.0 ] } } , { "box" : { "id" : "obj-25", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 30.0, 195.0, 20.0, 20.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-19", "maxclass" : "newobj", "numinlets" : 1, "numoutlets" : 2, "outlettype" : [ "bang", "int" ], "patching_rect" : [ 405.0, 225.0, 32.5, 20.0 ], "presentation_rect" : [ 241.0, 240.0, 0.0, 0.0 ], "text" : "t b i" } } , { "box" : { "id" : "obj-20", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 375.0, 300.0, 20.0, 20.0 ], "presentation_rect" : [ 211.0, 315.0, 0.0, 0.0 ] } } , { "box" : { "id" : "obj-21", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 405.0, 195.0, 20.0, 20.0 ], "presentation_rect" : [ 241.0, 210.0, 0.0, 0.0 ] } } , { "box" : { "id" : "obj-22", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 375.0, 195.0, 20.0, 20.0 ], "presentation_rect" : [ 211.0, 210.0, 0.0, 0.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-23", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 375.0, 270.0, 32.5, 20.0 ], "text" : "||" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-18", "maxclass" : "newobj", "numinlets" : 1, "numoutlets" : 2, "outlettype" : [ "bang", "int" ], "patching_rect" : [ 60.0, 405.0, 32.5, 20.0 ], "text" : "t b i" } } , { "box" : { "id" : "obj-15", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 60.0, 375.0, 20.0, 20.0 ] } } , { "box" : { "id" : "obj-13", "maxclass" : "toggle", "numinlets" : 1, "numoutlets" : 1, "outlettype" : [ "int" ], "parameter_enable" : 0, "patching_rect" : [ 30.0, 375.0, 20.0, 20.0 ] } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "id" : "obj-5", "maxclass" : "newobj", "numinlets" : 2, "numoutlets" : 1, "outlettype" : [ "int" ], "patching_rect" : [ 30.0, 435.0, 32.5, 20.0 ], "text" : "&&" } } , { "box" : { "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-4", "linecount" : 2, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 30.0, 90.0, 525.0, 33.0 ], "text" : "When using digital computers, one builds complicated decision-making procedures from simpler elements. The most simple building blocks for digital computation are the logical operators." } } , { "box" : { "bubble" : 1, "fontname" : "Arial", "fontsize" : 12.0, "frgb" : 0.0, "id" : "obj-2", "linecount" : 3, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 15.0, 15.0, 315.0, 51.0 ], "text" : "Patch 041. 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