Base 10

Base 2

Base 16

Base 2
Base 3
Base 4
Base 5
Base 6
Base 7
Base 8
Base 9
Base 10
Base 11
Base 12
Base 13

Base 14
Base 15
Base 16
Base 17
Base 18
Base 19
Base 20
Base 21
Base 22
Base 23
Base 24
Base 25

Base 26
Base 27
Base 28
Base 29
Base 30
Base 31
Base 32
Base 33
Base 34
Base 35
Base 36

Base Converter (Bin, Dec, Hex, etc.)

日本語 / English

Base conversion calculator with method of calculation. binary,decimal,octal,hex, from 2 to 36.

Doesn't support decimal fraction.

Posted on 2020-03-26

How to convert base

Base-N (non-decimal) to decimal

Multiply $N^0, N^1, ... N^n$ from the bottom of the base-N and add up.

e.g. When converting the binary number 1101100 to decimal number.

0 \times 2^0+0 \times 2^1 + 1 \times 2^2 + 1 \times 2^3 + 0 \times 2^4 + 1 \times 2^5 + 1 \times 2^6 + 0 = 108

e.g. When converting hexadecimal 6C to decimal (C = 12).

12 \times 16^0 + 6 \times 16^1 = 108

Decimal to base-N (non-decimal)

Divide the decimal number until the quotient is less than N.
Arrange the remainders in order from the end, with the last quotient at the top.

e.g. When converting decimal 108 to binary.
108 / 2 = 54, remainder of 0
54 / 2 = 27, remainder of 0
27 / 2 = 13, remainder of 1
13 / 2 = 6, remainder of 1
6 / 2 = 3, remainder of 0
3 / 2 = 1, remainder of 1
-> 1101100

In other words, the algorithm that decomposes into the following format.

0 + 0 \times 2 + 1 \times 2^2 + 1 \times 2^3 + 0 \times 2^4 + 1 \times 2^5 + 1 \times 2^6 + 0

e.g. When converting decimal 108 to hexadecimal.
108 / 16 = 6, remainder of 12 (C)
-> 6C

Cheat sheet

Dec (10)	Bin (2)	Qua (4)	Oct (8)	Hex (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	100	20	10