计╰参(Number Systems)

• 计膀Radix (or Base) -- # of unique symbols
• 家计Modulus -- # of unique quantities a given system can distinguish

9999 : Base = 10, Modulus = 10,000
• (Positional)╰参
• 秈 binary : 0 1
• 秈 octal : 0 1 2 3 4 5 6 7
• 秈 decimal : 0 1 2 3 4 5 6 7 8 9
• せ秈 hexadecimal : 0 1 2 3 4 5 6 7 8 9 A B C D E F
• Non-positional : Roman numerals
• 秈计╰参 Binary Number System
• じ bits - either 1 or 0
binary digit
• じ舱 byte - collection of 8 bits
• K or kilobyte - 1,024 bytes
• M or megabyte - 1,024 * 1,024 bytes
• G or gigabyte - 1,024 * 1,024 * 1,024 bytes

╰参ぇ锣传Conversion between Systems

1. Power Addition

           10012 = 8 + 0 + 0 + 1 = 9
   
           11.012 = 2 + 1 + 0 + 1/4 = 3.25
   
           A316 = 10 x 16 + 3 x 1 = 163
   

2. Radix Arithmetic

           273/8 = 34 ... 1
   	 34/8 =  4 ... 2
   
          27310 = 4218
   
          0.55 x 8 = 4.4    0.4 x 8 = 3.2    0.2 x 8 = 1.6    ...
   
           0.5510 = 0.431...8
           
   

3. Substitution

    oct       4   2   1
              |   |   |     
    binary   100,010,001
   
   
    hexa        A       3
                |       |     
    binary   1 0 1 0,0 0 1 1       舱
             1 0,1 0 0,0 1 1       舱, パ舱癬
               |    |     |     
    oct        2    4     3
    
             A316 = 101000112 = 2438