Hirota Yano / Programmer
Born in 1988, based in Japan

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

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

• Doesn't support decimal fraction.

## 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)

1. Divide the decimal number until the quotient is less than N.
2. 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