{"id":2579,"date":"2017-04-13T23:29:44","date_gmt":"2017-04-13T23:29:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&p=2579"},"modified":"2020-01-22T19:17:00","modified_gmt":"2020-01-22T19:17:00","slug":"assignment-historical-counting-systems-problem-set","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/assignment-historical-counting-systems-problem-set\/","title":{"raw":"Assignment: Historical Counting Systems Problem Set","rendered":"Assignment: Historical Counting Systems Problem Set"},"content":{"raw":"Counting Board And Quipu<\/strong>\r\n\r\n \r\n\r\n1)\u00a0\u00a0\u00a0\u00a0\u00a0 In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing.\r\n\r\n\"\"<\/a>\r\n\r\n2) \u00a0Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part a<\/strong> on the left and moving to the right for parts b<\/strong> through d<\/strong>.)\r\n

(a) 232<\/p>\r\n

(b) 5065<\/p>\r\n

(c) 23,451<\/p>\r\n

(d) 3002<\/p>\r\nBasic Base Conversions<\/strong>\r\n\r\n1)\u00a0\u00a0\u00a0\u00a0\u00a0 423 in base 5 to base 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 3044 in base 5 to base 10\r\n\r\n \r\n\r\n3)\u00a0\u00a0\u00a0\u00a0\u00a0 387 in base 10 to base 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4) 2546 in base 10 to base 5\r\n\r\n \r\n\r\nMayan Conversions<\/strong>\r\n\r\nConvert the following numbers to Mayan notation. Show your calculations used to get your answers.<\/em>\r\n\r\n \r\n\r\n1)\u00a0\u00a0\u00a0\u00a0\u00a0 135\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 234\r\n\r\n \r\n\r\n3)\u00a0\u00a0\u00a0\u00a0\u00a0 360\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4) 1,215\r\n\r\n \r\n\r\n5)\u00a0\u00a0\u00a0\u00a0\u00a0 10,500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6) 1,100,000\r\n\r\n \r\n\r\nConvert the following Mayan numbers to decimal (base<\/em>-10) numbers. Show all calculations.<\/em>\r\n\r\n\r\n\r\n
7)\r\n\r\n\"three<\/td>\r\n8)\r\n\r\n\"three<\/td>\r\n\r\n

9)\u00a0\"three<\/p>\r\n<\/td>\r\n

\u00a010)\r\n\r\n\"4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nJames Bidwell has suggested that Mayan addition was done by \u201csimply combining bars and dots and carrying to the next higher place.\u201d He goes on to say, \u201cAfter the combining of dots and bars, the second step is to exchange every five dots for one bar in the same position.\u201d After converting the following base 10 numbers into vertical Maya notation (in base 20, of course), perform the indicated addition:\r\n\r\n1)\u00a0\u00a0\u00a0\u00a0\u00a0 32 + 11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 82 + 15\r\n\r\n \r\n\r\n3)\u00a0\u00a0\u00a0\u00a0\u00a0 35 + 148 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04) 2412 + 5000\r\n\r\n \r\n\r\n5)\u00a0\u00a0\u00a0\u00a0\u00a0 450 + 844 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6) 10,000 + 20,000\r\n\r\n \r\n\r\n7)\u00a0\u00a0\u00a0\u00a0\u00a0 4,500 + 3,500 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a08) 130,000 + 30,000\r\n\r\n \r\n\r\n9)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Use the fact that the Mayans had a base-20 number system to complete the following multiplication table. The table entries should be in Mayan notation. Remember: Their zero looked like this\u2026. Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.<\/em>\r\n\r\n(To think about but not write up: Bidwell claims that only these entries are needed for \u201cMayan multiplication.\u201d What does he mean?)\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
 \r\n\r\nx<\/td>\r\n\u00a0\"one<\/a><\/td>\r\n\u00a0\"two<\/a><\/td>\r\n\u00a0\"three<\/a><\/td>\r\n\u00a0\"four<\/a><\/td>\r\n\u00a0\"one<\/a><\/td>\r\n\u00a0\"two<\/a><\/td>\r\n\u00a0\"three<\/a><\/td>\r\n<\/tr>\r\n
\"one<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\"two<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\"three<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\"four<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\"one<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\"two<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\"three<\/a><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\n \r\n\r\n \r\n\r\nBinary and Hexadecimal Conversions<\/strong>\r\n\r\nModern computers operate in a world of \u201con\u201d and \u201coff\u201d electronic switches, so use a binary<\/strong> counting system \u2013 base 2, consisting of only two digits: 0 and 1.<\/em>\r\n\r\n\u00a0<\/em><\/strong>\r\n\r\nConvert the following binary numbers to decimal (base<\/em>-10) numbers.<\/em>\r\n\r\n \r\n\r\n1)\u00a0\u00a0\u00a0\u00a0\u00a0 1001\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 1101\r\n\r\n \r\n\r\n3)\u00a0\u00a0\u00a0\u00a0\u00a0 110010\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4) 101110\r\n\r\n \r\n\r\nConvert the following base-10 numbers to binary<\/em>\r\n\r\n \r\n\r\n5)\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6) 12\r\n\r\n \r\n\r\n7)\u00a0\u00a0\u00a0\u00a0\u00a0 36\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8) 27\r\n\r\n \r\n\r\nFour binary digits together can represent any base-10 number from 0 to 15. To create a more human-readable representation of binary-coded numbers, hexadecimal numbers, base 16, are commonly used. Instead of using the 8,13,1216 notation used earlier, the letter A is used to represent the digit 10, B for 11, up to F for 15, so 8,13,1216 would be written as 8DC.<\/em>\r\n\r\n \r\n\r\nConvert the following hexadecimal numbers to decimal (base<\/em>-10) numbers.<\/em>\r\n\r\n\u00a0<\/em>\r\n\r\n9)\u00a0\u00a0\u00a0\u00a0\u00a0 C3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10) 4D\r\n\r\n \r\n\r\n11)\u00a0\u00a0\u00a0 3A6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12) BC2\r\n\r\nConvert the following base-10 numbers to hexadecimal<\/em>\r\n\r\n\u00a0<\/em>\r\n\r\n13)\u00a0\u00a0\u00a0\u00a0\u00a0 152 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 14) 176\r\n\r\n \r\n\r\n15)\u00a0\u00a0\u00a0\u00a0\u00a0 2034 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 16) 8263\r\n\r\n\u00a0<\/em>\r\n

Exploration<\/h3>\r\n \r\n\r\n1)\u00a0\u00a0\u00a0\u00a0\u00a0 What are the advantages and disadvantages of bases other than ten.\r\n\r\n \r\n\r\n2)\u00a0\u00a0\u00a0\u00a0\u00a0 Supposed you are charged with creating a base-15 number system. What symbols would you use for your system and why? Explain with at least two specific examples how you would convert between your base-15 system and the decimal system.\r\n\r\n \r\n\r\n3)\u00a0\u00a0\u00a0\u00a0\u00a0 Describe an interesting aspect of Mayan civilization that we did not discuss in class. Your findings must come from some source such as an encyclopedia article, or internet site and you must provide reference(s) of the materials you used (either the publishing information or Internet address).\r\n\r\n4) For a Papuan tribe in southeast New Guinea, it was necessary to translate the bible passage John 5:5 \u201cAnd a certain man was there, which had an infirmity 30 and 8 years\u201d into \u201cA man lay ill one man, both hands, five and three years.\u201d Based on your own understanding of bases systems (and some common sense), furnish an explanation of the translation. Please use complete sentences to do so. (Hint: To do this problem, I am asking you to think about how base systems work, where they come from, and how they are used. You won\u2019t necessarily find an \u201canswer\u201d in readings or such\u2026you\u2019ll have to think it through and come up with a reasonable response. Just make sure that you clearly explain why the passage was translated the way that it was.)\r\n\r\n \r\n\r\n5)\u00a0\u00a0\u00a0\u00a0\u00a0 The Mayan calendar was largely discussed leading up to December 2012. Research how the Mayan calendar works, and how the counts are related to the number based they use.\r\n\r\n \r\n\r\n ","rendered":"

Counting Board And Quipu<\/strong><\/p>\n

 <\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing.<\/p>\n

\"\"<\/a><\/p>\n

2) \u00a0Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part a<\/strong> on the left and moving to the right for parts b<\/strong> through d<\/strong>.)<\/p>\n

(a) 232<\/p>\n

(b) 5065<\/p>\n

(c) 23,451<\/p>\n

(d) 3002<\/p>\n

Basic Base Conversions<\/strong><\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 423 in base 5 to base 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 3044 in base 5 to base 10<\/p>\n

 <\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0 387 in base 10 to base 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4) 2546 in base 10 to base 5<\/p>\n

 <\/p>\n

Mayan Conversions<\/strong><\/p>\n

Convert the following numbers to Mayan notation. Show your calculations used to get your answers.<\/em><\/p>\n

 <\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 135\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 234<\/p>\n

 <\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0 360\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4) 1,215<\/p>\n

 <\/p>\n

5)\u00a0\u00a0\u00a0\u00a0\u00a0 10,500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6) 1,100,000<\/p>\n

 <\/p>\n

Convert the following Mayan numbers to decimal (base<\/em>-10) numbers. Show all calculations.<\/em><\/p>\n\n\n\n
7)<\/p>\n

\"three<\/td>\n

8)<\/p>\n

\"three<\/td>\n

\n

9)\u00a0\"three<\/p>\n<\/td>\n

\u00a010)<\/p>\n

\"4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

James Bidwell has suggested that Mayan addition was done by \u201csimply combining bars and dots and carrying to the next higher place.\u201d He goes on to say, \u201cAfter the combining of dots and bars, the second step is to exchange every five dots for one bar in the same position.\u201d After converting the following base 10 numbers into vertical Maya notation (in base 20, of course), perform the indicated addition:<\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 32 + 11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 82 + 15<\/p>\n

 <\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0 35 + 148 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04) 2412 + 5000<\/p>\n

 <\/p>\n

5)\u00a0\u00a0\u00a0\u00a0\u00a0 450 + 844 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6) 10,000 + 20,000<\/p>\n

 <\/p>\n

7)\u00a0\u00a0\u00a0\u00a0\u00a0 4,500 + 3,500 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a08) 130,000 + 30,000<\/p>\n

 <\/p>\n

9)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Use the fact that the Mayans had a base-20 number system to complete the following multiplication table. The table entries should be in Mayan notation. Remember: Their zero looked like this\u2026. Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.<\/em><\/p>\n

(To think about but not write up: Bidwell claims that only these entries are needed for \u201cMayan multiplication.\u201d What does he mean?)<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n
 <\/p>\n

x<\/td>\n

\u00a0\"one<\/a><\/td>\n\u00a0\"two<\/a><\/td>\n\u00a0\"three<\/a><\/td>\n\u00a0\"four<\/a><\/td>\n\u00a0\"one<\/a><\/td>\n\u00a0\"two<\/a><\/td>\n\u00a0\"three<\/a><\/td>\n<\/tr>\n
\"one<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\"two<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\"three<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\"four<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\"one<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\"two<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\"three<\/a><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

Binary and Hexadecimal Conversions<\/strong><\/p>\n

Modern computers operate in a world of \u201con\u201d and \u201coff\u201d electronic switches, so use a binary<\/strong> counting system \u2013 base 2, consisting of only two digits: 0 and 1.<\/em><\/p>\n

\u00a0<\/em><\/strong><\/p>\n

Convert the following binary numbers to decimal (base<\/em>-10) numbers.<\/em><\/p>\n

 <\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 1001\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2) 1101<\/p>\n

 <\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0 110010\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4) 101110<\/p>\n

 <\/p>\n

Convert the following base-10 numbers to binary<\/em><\/p>\n

 <\/p>\n

5)\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6) 12<\/p>\n

 <\/p>\n

7)\u00a0\u00a0\u00a0\u00a0\u00a0 36\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8) 27<\/p>\n

 <\/p>\n

Four binary digits together can represent any base-10 number from 0 to 15. To create a more human-readable representation of binary-coded numbers, hexadecimal numbers, base 16, are commonly used. Instead of using the 8,13,1216 notation used earlier, the letter A is used to represent the digit 10, B for 11, up to F for 15, so 8,13,1216 would be written as 8DC.<\/em><\/p>\n

 <\/p>\n

Convert the following hexadecimal numbers to decimal (base<\/em>-10) numbers.<\/em><\/p>\n

\u00a0<\/em><\/p>\n

9)\u00a0\u00a0\u00a0\u00a0\u00a0 C3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10) 4D<\/p>\n

 <\/p>\n

11)\u00a0\u00a0\u00a0 3A6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12) BC2<\/p>\n

Convert the following base-10 numbers to hexadecimal<\/em><\/p>\n

\u00a0<\/em><\/p>\n

13)\u00a0\u00a0\u00a0\u00a0\u00a0 152 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 14) 176<\/p>\n

 <\/p>\n

15)\u00a0\u00a0\u00a0\u00a0\u00a0 2034 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 16) 8263<\/p>\n

\u00a0<\/em><\/p>\n

Exploration<\/h3>\n

 <\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 What are the advantages and disadvantages of bases other than ten.<\/p>\n

 <\/p>\n

2)\u00a0\u00a0\u00a0\u00a0\u00a0 Supposed you are charged with creating a base-15 number system. What symbols would you use for your system and why? Explain with at least two specific examples how you would convert between your base-15 system and the decimal system.<\/p>\n

 <\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0 Describe an interesting aspect of Mayan civilization that we did not discuss in class. Your findings must come from some source such as an encyclopedia article, or internet site and you must provide reference(s) of the materials you used (either the publishing information or Internet address).<\/p>\n

4) For a Papuan tribe in southeast New Guinea, it was necessary to translate the bible passage John 5:5 \u201cAnd a certain man was there, which had an infirmity 30 and 8 years\u201d into \u201cA man lay ill one man, both hands, five and three years.\u201d Based on your own understanding of bases systems (and some common sense), furnish an explanation of the translation. Please use complete sentences to do so. (Hint: To do this problem, I am asking you to think about how base systems work, where they come from, and how they are used. You won\u2019t necessarily find an \u201canswer\u201d in readings or such\u2026you\u2019ll have to think it through and come up with a reasonable response. Just make sure that you clearly explain why the passage was translated the way that it was.)<\/p>\n

 <\/p>\n

5)\u00a0\u00a0\u00a0\u00a0\u00a0 The Mayan calendar was largely discussed leading up to December 2012. Research how the Mayan calendar works, and how the counts are related to the number based they use.<\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"author":17533,"menu_order":17,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2579","chapter","type-chapter","status-publish","hentry"],"part":192,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/2579","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/2579\/revisions"}],"predecessor-version":[{"id":2612,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/2579\/revisions\/2612"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/parts\/192"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/2579\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/media?parent=2579"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapter-type?post=2579"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/contributor?post=2579"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/license?post=2579"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}