Base eight is like base ten ... if you're missing two fingers --- Tom Lehrer from his novelty tune New Math
Let's add 10 to a number and see what we get!
0 + 10 = 10 | 0 | + |
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1 + 10 = 11 | + |
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2 + 10 = 12 | + |
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3 + 10 = 13 | + |
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4 + 10 = 14 | + |
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5 + 10 = 15 | + |
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6 + 10 = 16 | + |
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7 + 10 = 17 | + |
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8 + 10 = 18 | + |
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9 + 10 = 19 | + |
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10 + 10 = 20 | + |
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Let's add 12 in Octal to a number and see what we get!
0 + 10 = 12
1 + 10 = 13
2 + 10 = 14
3 + 10 = 15
4 + 10 = 16
5 + 10 = 17
6 + 10 = 20
7 + 10 = 21
10 + 10 = 22
11 + 10 = 23
12 + 10 = 24
Let's subtract 10 from a number and see what we get!
10 - 10 = 0 |
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11 - 10 = 1 |
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12 - 10 = 2 |
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13 - 10 = 3 |
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14 - 10 = 4 |
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15 - 10 = 5 |
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16 - 10 = 6 |
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17 - 10 = 7 |
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18 - 10 = 8 |
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19 - 10 = 9 |
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20 - 10 = 10 |
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Let's multiply 10 to a number and see what we get!
0 * 10 = 0
1 * 10 = 10
2 * 10 = 20
3 * 10 = 30
4 * 10 = 40
5 * 10 = 50
6 * 10 = 60
7 * 10 = 70
8 * 10 = 80
9 * 10 = 90
10 * 10 = 100
x | 10 | = | |||||||||
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x1 | =10 | ||||||||||
x2 | =20 | ||||||||||
x3 | =30 | ||||||||||
x4 | =40 | ||||||||||
x5 | =50 | ||||||||||
x6 | =60 | ||||||||||
x7 | =70 | ||||||||||
x8 | =80 | ||||||||||
x9 | =90 | ||||||||||
x10 | =100 |
Let's divide 10 from a number and see what we get!
100 / 10 = 10
90 / 10 = 9
80 / 10 = 8
70 / 10 = 7
60 / 10 = 6
50 / 10 = 5
40 / 10 = 4
30 / 10 = 3
20 / 10 = 2
10 / 10 = 1
0 / 10 = 0
Let's raise a number to the power of 10 and see what we get!
0 ^ 10 = 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.
1 ^ 10 = 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.
2 ^ 10 = 1,024; it's the same as 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.
3 ^ 10 = 59,049; it's the same as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.
4 ^ 10 = 1,048,576; it's the same as 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4.
5 ^ 10 = 9,765,625; it's the same as 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5.
6 ^ 10 = 60,466,176; it's the same as 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6.
7 ^ 10 = 282,475,249; it's the same as 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7.
8 ^ 10 = 1,073,741,824; it's the same as 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8.
9 ^ 10 = 3,486,784,401; it's the same as 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9.
10 ^ 10 = 10,000,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
Let's raise 10 to a power and see what we get!
10 ^ 0 = 1; a nonzero number raised to zero is 1.
10 ^ 1 = 10; it's the same as 10.
10 ^ 2 = 100; it's the same as 10 x 10.
10 ^ 3 = 1,000; it's the same as 10 x 10 x 10.
10 ^ 4 = 10,000; it's the same as 10 x 10 x 10 x 10.
10 ^ 5 = 100,000; it's the same as 10 x 10 x 10 x 10 x 10.
10 ^ 6 = 1,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10.
10 ^ 7 = 10,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10.
10 ^ 8 = 100,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
10 ^ 9 = 1,000,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
10 ^ 10 = 10,000,000,000; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
Let's add 1010 in Binary to a number and see what we get!
0 + 1010 = 1010
1 + 1010 = 1011
10 + 1010 = 1100
11 + 1010 = 1101
100 + 1010 = 1110
101 + 1010 = 1111
110 + 1010 = 10000
111 + 1010 = 10001
1000 + 1010 = 10010
1001 + 1010 = 10011
1010 + 1010 = 10100
Remember, just like in a computer, there are only zeros and ones, nothing
else.
Likewise, 2*5 is also 10 because you are adding five 2's together like this: 2+2+2+2+2, or like this:
You can also imagine that you can get 10 if you take the cube root of 1,000. Since this computer cannot display balls in 3-D, you'll have to get that many blocks, and build a base 10 by 10 and stack the blocks 10 high. You'll use exactly 1,000 blocks to build that perfect cube.
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