I. Numeral System

1. 十进制 Decimal

• base: 10
• 0 , 1, 2, 3, 4, 5, 6, 7, 8, 9

2. 二进制 Binary

• base: 2
• 0, 1
• begin with 0b

3. 八进制 Octonary

• base: 8
• 0, 1, 2, 3, 4, 5, 6, 7
• begin with 0

4. 十六进制 Hexadecimal

• base: 16
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• begin with 0x

II. Conversion between numeral system

1. Binary To Decimal

convert binary 0b1001 to decimal;

0b1001 = 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0
     = 8 + 0 + 0 + 1
     = 9

2. Decimal to Binary

convert decimal 20 to binary

Method 1

Use divsion and remainder

binary: divide by 2  -- remainder
20 / 2 = 10  -- 0
10 / 2 = 5   -- 0
5  / 2 = 2   -- 1
2  / 2 = 1   -- 0
1  / 2 = 0   -- 1
So binary = 0b10100

Method 2: 8421 code

20 = 1* 16 + 0 * 8 + 1 * 4 + 0 * 2 + 0 * 1
   = 10100
binary: 0b10100

3. Octonary to Decimal

convert octonary 01001 to decimal

01001 = 1 * 8^3 + 0 * 8^2 + 0 * 8^1 + 1 * 8^0
     = 512 + 0 + 0 + 1
     = 513

4. Decimal to Octonary

The same as decimal to binary, convert decimal 52 to octonary

52 / 8 = 6  -- 4
6 / 8  = 0  -- 6
octonary: 064

5. Hexadecimal to Decimal

convert hexadecimal 0x1001 to decimal

0x1001 = 1 * 16^3 + 0 * 16^2 + 0 * 16^1 + 1 * 16^0
     = 4096 + 0 + 0 + 1
     = 4097

6 Decimal to Hexadecimal

The same as decimal to binary, convert 52 to hexadecimal

52 / 16 = 3 -- 4
3 / 16  = 0 -- 3
hexadecimal: 0x34