TOOL/2020-03-26

DEC, BIN, HEX (Base 2-36) converter / Tool

Converts binary to 36 decimal numbers to other radixes.

Decimals are not supported.

Dec

Bin

Hex

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 Number Conversion Method

Since radix conversion only changes the notation of the number, the value will not change. However, this is only the case when dealing with integers, and is difficult when dealing with decimals. This tool and article do not support decimals.

Base-N (non-decimal) to decimal

Multiply each n-digit number by $N^0, N^1, ... N^n$ to compute the sum.

e.g. To convert 1101100 in binary to decimal.

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. To convert 6C in hexadecimal 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 last, with the last quotient at the top.

e.g. To convert 108 in decimal 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, an algorithm that decomposes into the following forms.

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. To convert 108 in decimal to hexadecimal.
108 / 16 = 6, remainder of 12 (C)
-> 6C

Cheat sheet

Dec (10)	Bin (2)	Qua (4)	Oct (8)	Hex (16)
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

Dec (10)	Bin (2)	Qua (4)	Oct (8)	Hex (16)
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