System Grab Bag

Base 2, 8, 10, 16, and 36 Converter

This tool allows you to convert numbers between different bases, specifically base 2, 8, 10, 16, and 36. Numbers can be written in many different forms. Most of the time in daily life, people use base 10, which has... well 10 digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
After the digit 9, a digit is added to the left and this previous digits wraps back around to 0, making 10. This is standard and trivial, however not all systems use these particular digits.

For example, binary uses only two digits 0 and 1, and is useful in computing as it can cleanly represent only 2 states, either off (0) or on (1). Therefore, the decimal number 2 is represented as 10 in binary. A slightly amusing joke goes somewhat like this:

There are only 10 types of people in the world: those that understand binary and those that don't.

You can combine these digits in different ways. For example, octal has 8 different states (2³). A Unix file mode is represented, in part, by 3 octal digits. Hexadecimal is yet another "extension" of this, having 16 different possible states (2⁴). But... since we only have 10 digits, how do we represent the other 6? We use letters. In addition to the 10 digits described above, we have 6 more:
A, B, C, D, E, F

Base 36 is another base used in some applications that need to compactly store long numbers. For example some websites use base 36 identifiers, which internally are just numeric, but having the public facing ID be in base 36 makes it easier to copy and paste a URL, without having to mix and match case. Base 36 has all 10 digits from base 10 and then all letters from A to Z.

Note that it is common to represent other numbers in a few different ways. You can but the radix (think base) as a subscript after a number (for example 10₁₆ is 16 in decimal). Another common way is to prefix the number with 0b for binary numbers, 0o for octal numbers, and 0x for hexadecimal numbers. The C programming language allows you to specify an octal number using a leading 0, however this can be confusing.

Base 2
Base 8
Base 10
Base 16
Base 36

Number Conversion Charts

0 to 36

Decimal Binary Octal Hexadecimal Base 36
0 0 0 0 0
1 1 1 1 1
2 10 2 2 2
3 11 3 3 3
4 100 4 4 4
5 101 5 5 5
6 110 6 6 6
7 111 7 7 7
8 1000 10 8 8
9 1001 11 9 9
10 1010 12 A A
11 1011 13 B B
12 1100 14 C C
13 1101 15 D D
14 1110 16 E E
15 1111 17 F F
16 10000 20 10 G
17 10001 21 11 H
18 10010 22 12 I
19 10011 23 13 J
20 10100 24 14 K
21 10101 25 15 L
22 10110 26 16 M
23 10111 27 17 N
24 11000 30 18 O
25 11001 31 19 P
26 11010 32 1A Q
27 11011 33 1B R
28 11100 34 1C S
29 11101 35 1D T
30 11110 36 1E U
31 11111 37 1F V
32 100000 40 20 W
33 100001 41 21 X
34 100010 42 22 Y
35 100011 43 23 Z
36 100100 44 24 10

Powers of 2

Decimal Binary Octal Hexadecimal
20 1 1 1 1
21 2 10 2 2
22 4 100 4 4
23 8 1000 10 8
24 16 10000 20 10
25 32 100000 40 20
26 64 1000000 100 40
27 128 10000000 200 80
28 256 100000000 400 100
29 512 1000000000 1000 200
210 1024 10000000000 2000 400
211 2048 100000000000 4000 800
212 4096 1000000000000 10000 1000
213 8192 10000000000000 20000 2000
214 16384 100000000000000 40000 4000
215 32768 1000000000000000 100000 8000
216 65536 10000000000000000 200000 10000

Powers of 2 (Larger Numbers)

Decimal Hexadecimal
231 2147483648 80000000
232 4294967296 100000000
263 9223372036854775808 8000000000000000
264 18446744073709551616 10000000000000000