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 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 |