1 00:00:08,400 --> 00:00:11,280 the most popular number system used 2 00:00:10,559 --> 00:00:13,759 today 3 00:00:11,280 --> 00:00:14,639 is the decimal system where the base is 4 00:00:13,759 --> 00:00:17,520 10. 5 00:00:14,639 --> 00:00:20,080 however for most of history another 6 00:00:17,520 --> 00:00:22,400 number system was more commonly used 7 00:00:20,080 --> 00:00:24,960 the sexagesimal system which has the 8 00:00:22,400 --> 00:00:26,960 base of 60. 9 00:00:24,960 --> 00:00:29,359 it was the preferred number system in 10 00:00:26,960 --> 00:00:31,359 astronomy in particular 11 00:00:29,359 --> 00:00:32,399 this system had been used by the 12 00:00:31,359 --> 00:00:35,600 babylonians 13 00:00:32,399 --> 00:00:37,280 during the 15th century bc and later by 14 00:00:35,600 --> 00:00:39,840 the greeks 15 00:00:37,280 --> 00:00:42,079 medieval islamic mathematicians although 16 00:00:39,840 --> 00:00:45,039 familiar with the decimal system 17 00:00:42,079 --> 00:00:47,200 most often use the sexagesimal system 18 00:00:45,039 --> 00:00:49,680 which they adapted and improved 19 00:00:47,200 --> 00:00:51,360 from the previous civilizations in this 20 00:00:49,680 --> 00:00:54,800 hexadecimal system 21 00:00:51,360 --> 00:00:57,920 one unit is 60 instead of 10. thus 22 00:00:54,800 --> 00:00:59,280 in this system we need 60 digits 0 23 00:00:57,920 --> 00:01:01,760 through 59 24 00:00:59,280 --> 00:01:02,399 while in the decimal system we only need 25 00:01:01,760 --> 00:01:04,159 10. 26 00:01:02,399 --> 00:01:06,880 an example of the use of this 27 00:01:04,159 --> 00:01:09,360 hexadecimal system in our everyday lives 28 00:01:06,880 --> 00:01:10,799 is the clock where 1 hour is divided 29 00:01:09,360 --> 00:01:13,119 into 60 minutes 30 00:01:10,799 --> 00:01:13,920 and one minute is divided into 60 31 00:01:13,119 --> 00:01:16,479 seconds 32 00:01:13,920 --> 00:01:18,720 after inheriting the sexagesimal system 33 00:01:16,479 --> 00:01:21,360 from babylonians and greeks 34 00:01:18,720 --> 00:01:23,119 islamic scholars improved and clarified 35 00:01:21,360 --> 00:01:25,759 the system 36 00:01:23,119 --> 00:01:27,600 similarly to the decimal number system 37 00:01:25,759 --> 00:01:28,400 after the contributions of islamic 38 00:01:27,600 --> 00:01:30,799 scholars 39 00:01:28,400 --> 00:01:33,759 the sexagesimal system essentially 40 00:01:30,799 --> 00:01:35,920 became the system we use today 41 00:01:33,759 --> 00:01:37,040 the babylonian system was used in 42 00:01:35,920 --> 00:01:40,479 mesopotamia 43 00:01:37,040 --> 00:01:41,920 around the year 2000 bc it was a 44 00:01:40,479 --> 00:01:44,560 positional system 45 00:01:41,920 --> 00:01:45,200 in which successive places of a numeral 46 00:01:44,560 --> 00:01:47,040 represent 47 00:01:45,200 --> 00:01:48,479 the success of power or positive 48 00:01:47,040 --> 00:01:51,280 integers of the base 49 00:01:48,479 --> 00:01:52,079 60 so it treated whole numbers and 50 00:01:51,280 --> 00:01:55,439 fractions 51 00:01:52,079 --> 00:01:55,759 in a unified manner the system only had 52 00:01:55,439 --> 00:01:57,920 two 53 00:01:55,759 --> 00:01:59,200 ciphers and no special mark for the 54 00:01:57,920 --> 00:02:02,079 unit's place 55 00:01:59,200 --> 00:02:03,119 leading to confusion because position 56 00:02:02,079 --> 00:02:06,000 values are not 57 00:02:03,119 --> 00:02:08,000 explicitly specified there was no way to 58 00:02:06,000 --> 00:02:10,479 distinguish between possible values 59 00:02:08,000 --> 00:02:10,800 represented by a given set of symbols in 60 00:02:10,479 --> 00:02:14,480 this 61 00:02:10,800 --> 00:02:17,520 system for example these two 62 00:02:14,480 --> 00:02:21,760 ciphers could represent either 1 and 1 3 63 00:02:17,520 --> 00:02:24,239 or 80 or many other possible values 64 00:02:21,760 --> 00:02:26,239 after the second century bc greek 65 00:02:24,239 --> 00:02:27,040 astronomers sought to alleviate some of 66 00:02:26,239 --> 00:02:29,599 the confusion 67 00:02:27,040 --> 00:02:31,840 created by only having two ciphers by 68 00:02:29,599 --> 00:02:32,560 using the 27 letters of the greek 69 00:02:31,840 --> 00:02:35,920 alphabet 70 00:02:32,560 --> 00:02:37,519 to represent numbers thus while these 71 00:02:35,920 --> 00:02:39,840 two ciphers could have indicated 72 00:02:37,519 --> 00:02:42,720 one-third in the babylonian system 73 00:02:39,840 --> 00:02:44,640 greeks simply used the letter k the 74 00:02:42,720 --> 00:02:47,599 babylonian and greek systems were 75 00:02:44,640 --> 00:02:49,680 refined by islamic mathematicians 76 00:02:47,599 --> 00:02:50,879 like the greek system islamic 77 00:02:49,680 --> 00:02:53,440 mathematicians used 78 00:02:50,879 --> 00:02:54,400 28 letters of the arabic alphabet as 79 00:02:53,440 --> 00:02:56,959 ciphers 80 00:02:54,400 --> 00:02:57,680 however while both the babylonians and 81 00:02:56,959 --> 00:03:00,800 the greeks 82 00:02:57,680 --> 00:03:03,519 lacked a differentiation of place values 83 00:03:00,800 --> 00:03:04,319 islamic mathematicians easily divided up 84 00:03:03,519 --> 00:03:06,400 the units 85 00:03:04,319 --> 00:03:07,599 and named the positions both in the 86 00:03:06,400 --> 00:03:10,640 fractional and whole 87 00:03:07,599 --> 00:03:13,599 part positive powers went from 88 00:03:10,640 --> 00:03:14,640 degrees first elevenths second elevates 89 00:03:13,599 --> 00:03:16,400 and so on 90 00:03:14,640 --> 00:03:18,080 while negative powers were called 91 00:03:16,400 --> 00:03:22,239 minutes seconds thirds 92 00:03:18,080 --> 00:03:25,440 etc each unit was comprised of 60 93 00:03:22,239 --> 00:03:25,440 of the previous unit 94 00:03:25,599 --> 00:03:31,680 the base of a sexadecimal number is 60 95 00:03:28,879 --> 00:03:32,000 thus a digit n in the unit's place 96 00:03:31,680 --> 00:03:34,879 called 97 00:03:32,000 --> 00:03:38,000 degrees is equal to the decimal number n 98 00:03:34,879 --> 00:03:40,000 times 60 to the power of zero 99 00:03:38,000 --> 00:03:41,280 decreasing from the units are the 100 00:03:40,000 --> 00:03:45,440 minutes seconds 101 00:03:41,280 --> 00:03:48,480 thirds etc the digit n in minutes place 102 00:03:45,440 --> 00:03:51,599 is equal to n divided by 60 103 00:03:48,480 --> 00:03:53,439 and seconds is equal to n divided by 60 104 00:03:51,599 --> 00:03:55,439 squared 105 00:03:53,439 --> 00:03:57,120 increasing from the units are the first 106 00:03:55,439 --> 00:04:00,319 elevates second elevates 107 00:03:57,120 --> 00:04:03,200 etc first elevates is equal to 108 00:04:00,319 --> 00:04:05,439 n times sixty to the power of one while 109 00:04:03,200 --> 00:04:08,959 second elevates is equal to n times 110 00:04:05,439 --> 00:04:08,959 sixty to the power of two 111 00:04:09,040 --> 00:04:12,879 thus the conversion chart for decimal to 112 00:04:11,599 --> 00:04:16,159 hexadecimal 113 00:04:12,879 --> 00:04:16,159 looks something like this 114 00:04:16,239 --> 00:04:20,000 let's look at a sexagesimal number in 115 00:04:18,320 --> 00:04:22,320 more detail 116 00:04:20,000 --> 00:04:23,120 here we have the number one second 117 00:04:22,320 --> 00:04:26,080 elevate 118 00:04:23,120 --> 00:04:28,800 six first elevates three degrees 15 119 00:04:26,080 --> 00:04:31,440 minutes and nine seconds 120 00:04:28,800 --> 00:04:32,960 using the chart we know that the value 121 00:04:31,440 --> 00:04:35,520 of this number is 122 00:04:32,960 --> 00:04:36,400 one times sixty squared plus six times 123 00:04:35,520 --> 00:04:38,240 sixty 124 00:04:36,400 --> 00:04:41,440 plus three times sixty to the power of 125 00:04:38,240 --> 00:04:45,520 zero plus fifteen divided by sixty 126 00:04:41,440 --> 00:04:45,520 plus nine divided by six c squared 127 00:04:46,080 --> 00:04:49,520 in order to convert the sexadecimal 128 00:04:48,240 --> 00:04:51,840 number to decimal 129 00:04:49,520 --> 00:04:53,040 we simply multiply all of the numbers 130 00:04:51,840 --> 00:04:56,160 with their bases 131 00:04:53,040 --> 00:05:00,560 and add them all together again 132 00:04:56,160 --> 00:05:03,600 this would be 3600 plus 360 133 00:05:00,560 --> 00:05:08,840 plus 3 plus 0.25 134 00:05:03,600 --> 00:05:11,840 plus 0.0025 all equaling to 135 00:05:08,840 --> 00:05:11,840 3963 136 00:05:14,639 --> 00:05:19,199 the cipherization and increased 137 00:05:16,639 --> 00:05:20,880 organization of the ancient sexagesimal 138 00:05:19,199 --> 00:05:22,080 system by medieval islamic 139 00:05:20,880 --> 00:05:24,720 mathematicians 140 00:05:22,080 --> 00:05:25,680 was a tremendously useful contribution 141 00:05:24,720 --> 00:05:35,600 that perfected 142 00:05:25,680 --> 00:05:35,600 the system