How to convert base
Base-N (non-decimal) to decimal
Multiply from the bottom of the base-N and add up.
e.g. When converting the binary number 1101100 to decimal number.
e.g. When converting hexadecimal 6C to decimal (C = 12).
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.
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 |