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So, let’s count in base 6

So, let’s count in base 6. Digits allowed: 0, 1, 2, 3, 4, 5 There is no such thing as 6 When we read a number such as 213 6 , we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”. Count! In base 6. 1, 2, 3, 4, 5,

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So, let’s count in base 6

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  1. So, let’s count in base 6 • Digits allowed: 0, 1, 2, 3, 4, 5 • There is no such thing as 6 • When we read a number such as 2136, we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”

  2. Count! In base 6 • 1, 2, 3, 4, 5, • 10, 11, 12, 13, 14, 15, • 20, 21, 22, 23, 24, 25, • 30, 31, 32, 33, 34, 35, • 40, 41, 42, 43, 44, 45, • 50, 51, 52, 53, 54, 55, • 100, 101, 102, 103, 104, 105, 110

  3. Digits 0 - 9 New place value after 9 in a given place Each place is 10 times as valuable as the one to the right 243 = 2 • (10 • 10) + 4 • 10 + 3 • 1 Digits 0 - 5 New place value after 5 in a given place Each place is 6 times as valuable as the one to the right. 243base 6 = 2 • (6 • 6) + 4 • 6 + 3 • 1 or 99 in base 10 Compare base 6 to base 10

  4. In base 6, write the first five place values. _____ _____ _____ _____ _____ 1296 216 36 6 1 64 63 62 61 60 cube flat long unit

  5. 312 =3 • 100 + 1 • 10 + 2 • 1 312base 6 = 3 • 36 + 1 • 6 + 2 • 1 = 116 in base 10 Compare Base 6 to Base 10

  6. How to change from Base 10 to Base 6. • Suppose your number is 325 in base 10. • We need to know what our place values will look like. • _____ _____ _____ _____ 6•6•6 6•6 6 1 Now, 6•6•6 = 216. 216 = 1000 in base 6.

  7. Base 10 to Base 6 • ___1__ _____ _____ _____ 6•6•6 6•6 6 1 • Now, 325 - 216 = 109. Since 109 is less than 216, we move to the next smaller place value: 6 • 6 = 36. • 109 - 36 = 73. Since 73 is greater than 36, we stay with the same place value.

  8. Base 10 to Base 6 • __1___ ___3__ _____ _____ 6•6•6 6•6 6 1 • We had 109: 109 - 36 - 36 - 36 = 1. We subtracted 36 three times, so 3 goes in the 36ths place. • We have 1 left. 1 is less than 6, so there are no 6s. Just a 1 in the units place.

  9. Base 10 to Base 6 • __1___ ___3__ __0___ __1___ 6•6•6 6•6 6 1 • Check: 1 • 216 + 3 • 36 + 1 • 1 = 325

  10. Count! In base 16 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 2c, 2d, 2e, 2f

  11. In base 16, write the first five place values. ______ _____ _____ _____ _____ 65,536 4096 256 16 1 164 163 162 161 160

  12. In base 5, write the first five place values. _____ _____ _____ _____ _____ 625 125 25 5 1 54 53 52 51 50 cube flat long unit

  13. In base 2, write the first five place values. _____ _____ _____ _____ _____ 16 8 4 2 1 24 23 22 21 20

  14. Let’s Look at Adding and Subtracting in Alphabitia • If we use the Alphabitian numerals, do our rules for addition and subtraction hold true? • Warm up: tell me one more and one less of each • AB • CAD • B0B • AA0 • DD • Use manipulatives or drawings to explain your answers.

  15. Let’s add in Alphabitia BCD+ DB BCD is DB is BCD + DB is

  16. You try: B0B+ABC Use the manipulatives or draw pictures to help explain your answer.

  17. Let’s subtract CBD - ADC = CBD is ADC is CBD - ADC is

  18. You Try… D00-B0B B0A-BD

  19. You try: Use manipulatives or drawings to explain BBC- A0C A0A0D- BCA

  20. First Exam Scheduled • Wednesday, February 13th • Cover material from: • Textbook: 1.2, 1.3, 1.4, 1.7, 2.3, 3.1, 3.2 • Explorations: 1.1, 1.4, 1.7, 2.8, 2.9, 3.1, 3.6 • Notes/Problems from class • Sample test questions on line next Monday.

  21. Homework for Monday • Exploration 2.9: Part 1: for Base 6, 2, and 16, do #2; Part 3: #2, 3; Part 4: #1, 2, 4. • Read Textbook pp. 109-118 • Do Textbook Problems pp. 120 - 121: 15b,c, 16b,d, 17a,i, 18b,f, 19, 29

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