Base eight is like base ten ... if you're missing two fingers --- Tom Lehrer from his novelty tune New Math
Let's add 8 to a number and see what we get!
0 + 8 = 8
0
+
=
1 + 8 = 9
+
=
2 + 8 = 10
+
=
3 + 8 = 11
+
=
4 + 8 = 12
+
=
5 + 8 = 13
+
=
6 + 8 = 14
+
=
7 + 8 = 15
+
=
8 + 8 = 16
+
=
9 + 8 = 17
+
=
10 + 8 = 18
+
=
Let's add 10 in Octal to a number and see what we get!
0 + 10 = 10
1 + 10 = 11
2 + 10 = 12
3 + 10 = 13
4 + 10 = 14
5 + 10 = 15
6 + 10 = 16
7 + 10 = 17
10 + 10 = 20
11 + 10 = 21
12 + 10 = 22
Let's subtract 8 from a number and see what we get!
8 - 8 = 0
-
=
0
9 - 8 = 1
-
=
10 - 8 = 2
-
=
11 - 8 = 3
-
=
12 - 8 = 4
-
=
13 - 8 = 5
-
=
14 - 8 = 6
-
=
15 - 8 = 7
-
=
16 - 8 = 8
-
=
17 - 8 = 9
-
=
18 - 8 = 10
-
=
Let's multiply 8 to a number and see what we get!
0 * 8 = 0
1 * 8 = 8
2 * 8 = 16
3 * 8 = 24
4 * 8 = 32
5 * 8 = 40
6 * 8 = 48
7 * 8 = 55
8 * 8 = 64
9 * 8 = 72
10 * 8 = 80
x | 8 | = | |||||||
---|---|---|---|---|---|---|---|---|---|
x1 | =8 | ||||||||
x2 | =16 | ||||||||
x3 | =24 | ||||||||
x4 | =32 | ||||||||
x5 | =40 | ||||||||
x6 | =48 | ||||||||
x7 | =56 | ||||||||
x8 | =64 | ||||||||
x9 | =72 | ||||||||
x10 | =80 |
Let's divide 8 from a number and see what we get!
80 / 8 = 10
72 / 8 = 9
64 / 8 = 8
56 / 8 = 7
48 / 8 = 6
40 / 8 = 5
32 / 8 = 4
24 / 8 = 3
16 / 8 = 2
8 / 8 = 1
0 / 8 = 0
Let's raise a number to the power of 8 and see what we get!
0 ^ 8 = 0
1 ^ 8 = 1
2 ^ 8 = 256
3 ^ 8 = 6,561
4 ^ 8 = 65,536
5 ^ 8 = 390,625
6 ^ 8 = 1,679,616
7 ^ 8 = 5,764,801
8 ^ 8 = 16,777,216
9 ^ 8 = 43,046,721
10 ^ 8 = 100,000,000
Let's raise 8 to a power and see what we get!
8 ^ 0 = 1
8 ^ 1 = 8
8 ^ 2 = 64
8 ^ 3 = 512
8 ^ 4 = 4,096
8 ^ 5 = 32,768
8 ^ 6 = 262,144
8 ^ 7 = 2,097,152
8 ^ 8 = 16,777,216
8 ^ 9 = 134,217,728
8 ^ 10 = 1,073,741,824
Let's add 1000 in Binary to a number and see what we get!
0 + 1000 = 1000
1 + 1000 = 1001
10 + 1000 = 1010
11 + 1000 = 1011
100 + 1000 = 1100
101 + 1000 = 1101
110 + 1000 = 1110
111 + 1000 = 1111
1000 + 1000 = 10000
1001 + 1000 = 10001
1010 + 1000 = 10010
Remember, just like in a computer, there are only zeros and ones, nothing
else.
Likewise, 2*4 is also 8 because you are adding four 2's together like this: 2+2+2+2, or like this:
Or to break it down even further,
(2*2)*2 = (2+2)*2 = (2+2)+(2+2) = 2+2+2+2 = 8
If 2^3=8, does 3^2=8 also? Let's see here:
You can also imagine that you can get 8 if you take the cube root of 512. Since this computer cannot display balls in 3-D, you'll have to get that many blocks, and build a base 8 by 8 and stack the blocks 8 high. You'll use exactly 512 blocks to build that perfect cube.
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