Base eight is like base ten ... if you're missing two fingers --- Tom Lehrer from his novelty tune New Math
Let's add 9 to a number and see what we get!
0 + 9 = 9
0
+
=
1 + 9 = 10
+
=
2 + 9 = 11
+
=
3 + 9 = 12
+
=
4 + 9 = 13
+
=
5 + 9 = 14
+
=
6 + 9 = 15
+
=
7 + 9 = 16
+
=
8 + 9 = 17
+
=
9 + 9 = 18
+
=
10 + 9 = 19
+
=
Let's add 11 in Octal to a number and see what we get!
0 + 11 = 11
1 + 11 = 12
2 + 11 = 13
3 + 11 = 14
4 + 11 = 15
5 + 11 = 16
6 + 11 = 17
7 + 11 = 20
10 + 11 = 21
11 + 11 = 22
12 + 11 = 23
Let's subtract 9 from a number and see what we get!
9 - 9 = 0
-
=
0
10 - 9 = 1
-
=
11 - 9 = 2
-
=
12 - 9 = 3
-
=
13 - 9 = 4
-
=
14 - 9 = 5
-
=
15 - 9 = 6
-
=
16 - 9 = 7
-
=
17 - 9 = 8
-
=
18 - 9 = 9
-
=
19 - 9 = 10
-
=
Let's multiply 9 to a number and see what we get!
0 * 9 = 0
1 * 9 = 9
2 * 9 = 18
3 * 9 = 27
4 * 9 = 36
5 * 9 = 45
6 * 9 = 54
7 * 9 = 63
8 * 9 = 72
9 * 9 = 81
10 * 9 = 90
x | 9 | = | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
x1 | =9 | |||||||||
x2 | =18 | |||||||||
x3 | =27 | |||||||||
x4 | =36 | |||||||||
x5 | =45 | |||||||||
x6 | =54 | |||||||||
x7 | =63 | |||||||||
x8 | =72 | |||||||||
x9 | =81 | |||||||||
x10 | =90 |
Let's divide 9 from a number and see what we get!
90 / 9 = 10
81 / 9 = 9
72 / 9 = 8
63 / 9 = 7
54 / 9 = 6
45 / 9 = 5
36 / 9 = 4
27 / 9 = 3
18 / 9 = 2
9 / 9 = 1
0 / 9 = 0
Let's raise a number to the power of 9 and see what we get!
0 ^ 9 = 0
1 ^ 9 = 1
2 ^ 9 = 512
3 ^ 9 = 19,683
4 ^ 9 = 262,144
5 ^ 9 = 1,953,125
6 ^ 9 = 10,077,696
7 ^ 9 = 40,353,607
8 ^ 9 = 134,217,728
9 ^ 9 = 387,420,489
10 ^ 9 = 1,000,000,000
Let's raise 9 to a power and see what we get!
9 ^ 0 = 1
9 ^ 1 = 9
9 ^ 2 = 81
9 ^ 3 = 729
9 ^ 4 = 6,561
9 ^ 5 = 59,049
9 ^ 6 = 531,441
9 ^ 7 = 4,782,969
9 ^ 8 = 43,046,721
9 ^ 9 = 387,420,489
9 ^ 10 = 3,486,784,401
Let's add 1001 in Binary to a number and see what we get!
0 + 1001 = 1001
1 + 1001 = 1010
10 + 1001 = 1011
11 + 1001 = 1100
100 + 1001 = 1101
101 + 1001 = 1110
110 + 1001 = 1111
111 + 1001 = 10000
1000 + 1001 = 10001
1001 + 1001 = 10010
1010 + 1001 = 10011
Remember, just like in a computer, there are only zeros and ones, nothing
else.
Likewise, 3*3 is also 9 because you are adding three 3's together like this: 3+3+3, or like this:
Or to break it down even further,
3*3 = 3+3+3 = 9
If 3^2=9, does 2^3=8 also? Let's see here:
You can also imagine that you can get 9 if you take the cube root of 729. Since this computer cannot display balls in 3-D, you'll have to get that many blocks, and build a base 9 by 9 and stack the blocks 9 high. You'll use exactly 729 blocks to build that perfect cube.
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