Base eight is like base ten ... if you're missing two fingers --- Tom Lehrer from his novelty tune New Math
Let's add 12 to a number and see what we get!
0 + 12 = 12 | 0 | + |
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1 + 12 = 13 | + |
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2 + 12 = 14 | + |
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3 + 12 = 15 | + |
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4 + 12 = 16 | + |
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5 + 12 = 17 | + |
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6 + 12 = 18 | + |
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7 + 12 = 19 | + |
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8 + 12 = 20 | + |
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9 + 12 = 21 | + |
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10 + 12 = 22 | + |
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Let's add 14 in Octal to a number and see what we get!
0 + 14 = 14
1 + 14 = 15
2 + 14 = 16
3 + 14 = 17
4 + 14 = 20
5 + 14 = 21
6 + 14 = 22
7 + 14 = 23
10 + 14 = 24
11 + 14 = 25
12 + 14 = 26
Let's subtract 12 from a number and see what we get!
12 - 12 = 0 |
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13 - 12 = 1 |
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14 - 12 = 2 |
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15 - 12 = 3 |
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16 - 12 = 4 |
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17 - 12 = 5 |
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18 - 12 = 6 |
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19 - 12 = 7 |
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20 - 12 = 8 |
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21 - 12 = 9 |
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22 - 12 = 10 |
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Let's multiply 12 to a number and see what we get!
0 * 12 = 0
1 * 12 = 12
2 * 12 = 24
3 * 12 = 36
4 * 12 = 48
5 * 12 = 60
6 * 12 = 72
7 * 12 = 84
8 * 12 = 96
9 * 12 = 108
10 * 12 = 120
11 * 12 = 132
12 * 12 = 144
x | 12 | = | |||||||||||
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x1 | =12 | ||||||||||||
x2 | =24 | ||||||||||||
x3 | =36 | ||||||||||||
x4 | =48 | ||||||||||||
x5 | =60 | ||||||||||||
x6 | =72 | ||||||||||||
x7 | =84 | ||||||||||||
x8 | =96 | ||||||||||||
x9 | =108 | ||||||||||||
x10 | =120 |
Let's divide 12 from a number and see what we get!
120 / 12 = 10
108 / 12 = 9
96 / 12 = 8
84 / 12 = 7
72 / 12 = 6
60 / 12 = 5
48 / 12 = 4
36 / 12 = 3
24 / 12 = 2
12 / 12 = 1
0 / 12 = 0
Let's raise a number to the power of 12 and see what we get!
0 ^ 12 = 0; 0 raised to any nozero positive number is 0; it's the same as 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0.
1 ^ 12 = 1; 1 raised to any power is 1; it's the same as 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1.
2 ^ 12 = 4,096; it's the same as 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.
3 ^ 12 = 531,441; it's the same as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.
4 ^ 12 = 16,777,216; it's the same as 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4.
5 ^ 12 = 244,140,625; it's the same as 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5.
6 ^ 12 = 2,176,782,336; it's the same as 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6.
7 ^ 12 = 13,841,287,201; it's the same as 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7.
8 ^ 12 = 68,719,476,736; it's the same as 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8.
9 ^ 12 = 282,429,536,481; it's the same as 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9.
10 ^ 12 = 1,000,000,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
Let's raise 12 to a power and see what we get!
12 ^ 0 = 1; a nonzero number raised to zero is 1.
12 ^ 1 = 12; it's the same as 12.
12 ^ 2 = 144; it's the same as 12 x 12.
12 ^ 3 = 1,728; it's the same as 12 x 12 x 12.
12 ^ 4 = 20,736; it's the same as 12 x 12 x 12 x 12.
12 ^ 5 = 248,832; it's the same as 12 x 12 x 12 x 12 x 12.
12 ^ 6 = 2,985,984; it's the same as 12 x 12 x 12 x 12 x 12 x 12.
12 ^ 7 = 35,831,808; it's the same as 12 x 12 x 12 x 12 x 12 x 12 x 12.
12 ^ 8 = 429,981,696; it's the same as 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12.
12 ^ 9 = 5,159,780,352; it's the same as 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12.
12 ^ 10 = 61,917,364,224; it's the same as 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12.
Let's add 1100 in Binary to a number and see what we get!
0 + 1100 = 1100
1 + 1100 = 1101
10 + 1100 = 1110
11 + 1100 = 1111
100 + 1100 = 10000
101 + 1100 = 10001
110 + 1100 = 10010
111 + 1100 = 10011
1000 + 1100 = 10100
1001 + 1100 = 10101
1010 + 1100 = 10110
1011 + 1100 = 10111
1100 + 1100 = 11000
Remember, just like in a computer, there are only zeros and ones, nothing
else.
Likewise, 2*6 is also 12 because you are adding six 2's together like this: 2+2+2+2+2+2, or like this:
Likewise, 3*4 is also 12 because you are adding four 3's together like this: 3+3+3+3, or like this:
You can also imagine that you can get 12 if you take the cube root of 1,728. Since this computer cannot display balls in 3-D, you'll have to get that many blocks, and build a base 12 by 12 and stack the blocks 12 high. You'll use exactly 1,728 blocks to build that perfect cube.
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