Introduction to Computer Science notes - digital system

　　The digital system is a digital system with different symbols, in particular into the position location system and non-system

1. System location
   symbol determines the position occupied by the value of its representation in the system is represented by:
   
   
   1. Decimal System
      decimal b is 10, and the character set used to represent 0-9.
      
      
      1. Integer: use position of a rear below
         

      2. REAL: below the binary

         

   2. Binary system
      binary 0 and b is only 12 characters, in a computer program and data by 0's and 1's (the book using a bit string, i.e. string of bits), because it is the most basic computer hardware the principle is electronic switches, different representatives of different switching state.

      1. Integer
         We can be expressed as b is an integer of 2 bit string
         
      2. Real numbers
         can be divided into two parts real, integer part and a fractional part
         

          Note that the decimal expression of the latter method in fact, the number is represented in binary position, is a specific value, by definition, a representative of the fractional power is -1 if 1 is 2 * 1, that is 0.5, when decimal behind to pay attention to this point.

   3. Hex
      Binary Although it is used for an external display on the computer's internal storage data, due to the length and decimal conversion limitations and inconvenience, so with hexadecimal and octal.
      In hexadecimal, b is 16, a character set from 0 to 9, A to F
      
      1. 　　Integer
         
         

         And the other is basically the same band

      2. Real
         integer part and above, the fractional part of the position of the system according to the equation if the number is negative primary side 1 * 16, is converted to a decimal 0.0625.

   4. Octal
      b 8, character set 0-7

      1. 　　Integer
         

      2. 　　Real numbers
         and hexadecimal similar
         
         

   5. to sum up
      

       

      

       

2. Conversion between the various binary
   Either binary transformations that follow the formula in the system.
   Other binary conversion to decimal　　
   

    

   Binary Coded Decimal && && decimal from hexadecimal convert hexadecimal to octal
   

    

    

    Decimal to binary conversion between other
   first determine the uml diagram is just beginning is difficult to understand, but the actual step is to continue with other books in decimal hexadecimal b, the remainder is the goal, that is, under the figure of destination, if there is In addition to business again, until divisible.
   　　
   
   Specific examples of the three books
   
   
   
   on the decimal part, may be used in the multiplication (repetitive multiplication), the decimal fraction portion multiplied by the respective binary constant, b, the integer part of the result is the goal, the integer part if not, it is 0 , followed by the next b.
   

    

    

    

    

    

    Binary Hex
   earlier mentioned precisely because the binary display, so the invention hexadecimal and octal, binary because the four happens to be in a hexadecimal
   

    

    Binary octal
   
   
   
   

    

　　Non-location systems
　　　　Roman numerals: straight here posted about representation, interested can directly buy books.