Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using...
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Transcript of Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using...
![Page 1: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/1.jpg)
ζBasesDr Frost
Objectives: 1. To appreciate how we can have different number systems using
different ‘bases’.2. To convert numbers from decimal to another base.3. To convert numbers from any base to decimal.
![Page 2: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/2.jpg)
1001100101
11010001
96E854
FFBA4D
000000
1295823
8409284
These are all examples of numbers!What connects each group of numbers?
10
942
![Page 3: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/3.jpg)
Base
The base of a number system is the number of possible values for each digit.
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Values for each digit
Base Name of number system
0 to 9 10 Decimal0 to 1 2 Binary0 to F(A=10, B=11, ... F=15)
16 Hexadecimal
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Numbers in decimal
If we were to write out 2493, what is the value of each digit?
2 4 9 31000 100 10 1
2000 +400 +90 + 3 = 2493
multiply
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Numbers in decimal
Now suppose we had a number in base 5 instead. How do we convert it to decimal?
4 3 0 1 125 25 5 1
500 + 75 + 0 + 1 = 576
multiply
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![Page 6: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/6.jpg)
Numbers in decimal
Copy and complete in your book.
1 0 1 12
8 4 2 1
8 + 0 + 2 + 1 = 11?
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3 3 0 24
64 16 4 1
192 + 48 + 0 + 2 = 242
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The small number indicates the base.
1 2 2 03
27 9 3 1
27 + 18 + 6 + 0 = 51
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I’m a Mayan, Get
Me Out Of Here!
(Switch to ‘I’m a Mayan’ slides)
![Page 8: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/8.jpg)
Exercises
Original number In base 10 (decimal)11012 13
1112 7
1100112 51
10223 35
7348 476
2345 69
5306 198
Base 2 ?
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![Page 9: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/9.jpg)
Converting FROM decimal to other bases
Do the opposite! Convert 18 to binary.
1 0 0 1 0 2
16 8 4 2 1?
16 + 0 + 0 + 2 + 0 = 18? ? ? ? ?
![Page 10: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/10.jpg)
Converting FROM decimal to other bases
Convert 272 to base 5.
2 0 4 2 5
125 25 5 1?
250+ 0 + 20+ 2= 272? ? ? ?
![Page 11: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/11.jpg)
Converting FROM decimal to other bases
It can help to write out multiples of your various powers. Below is base 6.
Multiples of 6 Multiples of 62 Multiples of 63
612182430
3672108144180
2164326488641080
x 1
x 2
x 3
x 4
x 5
Therefore what is 800 is base 6?3412?
![Page 12: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/12.jpg)
Exercises
Decimal Binary Base 63 11 38 100 1210 1010 1477 1001101 205102 1100110 250105 1101001 2531365 10101010101 10153
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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
![Page 14: Ζ Bases Dr Frost Objectives: 1.To appreciate how we can have different number systems using different ‘bases’. 2.To convert numbers from decimal to another.](https://reader036.fdocuments.in/reader036/viewer/2022062417/551be8d0550346b9588b61cd/html5/thumbnails/14.jpg)
0 255 0
0 0 0
255 255 255
RED GREEN BLUE
255 255 0
75 172 198
255 128 0
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HEXADECIMAL
FF, FF, FF
00, 00, 00
00, FF, 00
FF, FF, 00
4B, AC, C6
FF, 80, 00
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0: 01: 162: 323: 484: 645: 806: 967: 1128: 1289: 144A: 160B: 176C: 192D: 208E: 224F: 240
Multiples of 16:
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Exercises
Provided worksheet.
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Adding in other bases
1 0 0 1+ 1 1 0 1
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Adding in other bases
1 0 1 0+ 1 1 0 1 1
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Multiplying in other bases
1 0 1 0 x 1 0 1
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QQQ Time
The number of possible values each digit can have.
1a
1b Because each digit must be between 0 and one less than the base/the digits must be less than the base.
2a 2
2b 178
3 551
4
5
6
7
8
3900
11011
240
100100
a = 2, b = 4
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