Larger Counting Example
Decimal (base 10) |
|
Binary (Base 2) |
(Base 4) |
Octal (Base 8) |
Hexadecimal (Base 16) |
0 |
|
0 |
0 |
0 |
0 |
1 |
|
1 |
1 |
1 |
1 |
2 |
|
10 |
2 |
2 |
2 |
3 |
|
11 |
3 |
3 |
3 |
4 |
|
100 |
10 |
4 |
4 |
5 |
|
101 |
11 |
5 |
5 |
6 |
|
110 |
12 |
6 |
6 |
7 |
|
111 |
13 |
7 |
7 |
8 |
|
1000 |
20 |
10 |
8 |
9 |
|
1001 |
21 |
11 |
9 |
10 |
|
1010 |
22 |
12 |
A |
11 |
|
1011 |
23 |
13 |
B |
12 |
|
1100 |
30 |
14 |
C |
13 |
|
1101 |
31 |
15 |
D |
14 |
|
1110 |
32 |
16 |
E |
15 |
|
1111 |
33 |
17 |
F |
16 |
|
10000 |
40 |
20 |
10 |
17 |
|
10001 |
41 |
21 |
11 |
18 |
|
10010 |
42 |
22 |
12 |
19 |
|
10011 |
43 |
23 |
13 |
20 |
|
10100 |
50 |
24 |
14 |
21 |
|
10101 |
51 |
25 |
15 |
22 |
|
10110 |
52 |
26 |
16 |
23 |
|
10111 |
53 |
27 |
17 |
24 |
|
11000 |
60 |
30 |
18 |
25 |
|
11001 |
61 |
31 |
19 |
26 |
|
11010 |
62 |
32 |
1A |
27 |
|
11011 |
63 |
33 |
1B |
28 |
|
11100 |
70 |
34 |
1C |
29 |
|
11101 |
71 |
35 |
1D |
30 |
|
11110 |
72 |
36 |
1E |
31 |
|
11111 |
73 |
37 |
1F |
32 |
|
100000 |
80 |
40 |
20 |
The Really Easy Stuff, part 1: Binary to Octal
10111012 converts to ?8
Divide the number into blocks of three, starting from the right. If you don’t have enough numbers, add 0s to the left.
001 011 101
Put a short powers-of-two number line above each of the blocks of three; remember, the 1s and 0s always go under the powers-of-two number line.
4 2 1 |
4 2 1 |
4 2 1 |
0 0 1 |
0 1 1 |
1 0 1 |
Add the value under the successes (1s).
4 2 1 |
4 2 1 |
4 2 1 |
0 0 1 |
0 1 1 |
1 0 1 |
1 |
3 |
5 |
There’s our number! 10111012 converts to 1358