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Bases

ζ. Dr Frost. Bases. Objectives: To appreciate how we can have different number systems using different ‘bases’. To convert numbers from decimal to another base. To convert numbers from any base to decimal. These are all examples of numbers !. What connects each group of numbers?.

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Bases

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  1. ζ Dr Frost Bases Objectives: To appreciate how we can have different number systems using different ‘bases’. To convert numbers from decimal to another base. To convert numbers from any base to decimal.

  2. These are all examples of numbers! What connects each group of numbers? 96E854 1001100101 11010001 FFBA4D 10 000000 942 12958 23 8409284

  3. Base ! The base of a number system is the number of possible values for each digit. ? ? ? ? ? ?

  4. Numbers in decimal If we were to write out 2493, what is the value of each digit? 1000 100 10 1 ? 2 4 9 3 multiply ? 2000 +400 +90 + 3 = 2493 ?

  5. Numbers in decimal Now suppose we had a number in base 5 instead. How do we convert it to decimal? 125 25 5 1 ? 4 3 0 1 multiply ? ? 500 + 75 + 0 + 1 = 576

  6. Numbers in decimal Copy and complete in your book. ? The small number indicates the base. ? 8 4 2 1 64 16 4 1 1 0 1 12 3 3 0 24 8 + 0 + 2 + 1 = 11 192 + 48 + 0 + 2 = 242 ? ? ? 27 9 3 1 1 2 2 03 27 + 18 + 6 + 0 = 51 ?

  7. I’m a Mayan, Get Me Out Of Here! (Switch to ‘I’m a Mayan’ slides)

  8. Exercises ? Base 2 ? ? ? ? ? ?

  9. Converting FROM decimal to other bases Do the opposite! Convert 18 to binary. ? 16 8 4 2 1 1 0 0 1 0 2 ? ? ? ? ? 16 + 0 + 0 + 2 + 0 = 18

  10. Converting FROM decimal to other bases Convert 272 to base 5. ? 125 25 5 1 2 0 4 2 5 ? ? ? ? 250+ 0 + 20+ 2= 272

  11. Converting FROM decimal to other bases It can help to write out multiples of your various powers. Below is base 6. Multiples of 63 Multiples of 6 Multiples of 62 x 1 6 12 18 24 30 36 72 108 144 180 216 432 648 864 1080 x 2 x 3 x 4 x 5 Therefore what is 800 is base 6? 3412 ?

  12. Exercises ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  13. Decimal to Hexadecimal The most well-known usage of hexadecimal is to represent colours. Each colour can be composed of red, green and blue light, each of intensity varying between 0 and 255. ...which can be represented using just 6 digits in hexadecimal, 2 for each of the three colour components. A means 10, B means 11, ... F means 15

  14. Multiples of 16: RED GREEN BLUE HEXADECIMAL 255 255 255 FF, FF, FF 0: 0 1: 16 2: 32 3: 48 4: 64 5: 80 6: 96 7: 112 8: 128 9: 144 A: 160 B: 176 C: 192 D: 208 E: 224 F: 240 0 ? ? 0 ? 0 00, 00, 00 ? ? 0 ? 255 ? 0 00, FF, 00 ? ? 255 ? 255 ? 0 ? FF, FF, 00 75 ? ? 172 198 ? ? 4B, AC, C6 255 ? ? 128 ? 0 ? FF, 80, 00

  15. Exercises Provided worksheet.

  16. Adding in other bases 1 0 0 1 + 1 1 0 1

  17. Adding in other bases 1 0 1 0 + 1 1 0 1 1

  18. Multiplying in other bases 1 0 1 0 x 1 0 1

  19. QQQ Time ? 3900 4 1a The number of possible values each digit can have. ? 11011 5 ? ? Because each digit must be between 0 and one less than the base/the digits must be less than the base. 1b 6 240 ? 100100 7 ? 2a 2 ? 8 a = 2, b = 4 ? ? 178 2b 551 3 ?

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