Thursday, March 5, 2015

Number Systems

When we type some letters , numbers or words, the computer decipher them in numbers as computer only understands it. Therefore, number system is used to represent digital data and the digital data is represented by symbols called digits.

The Number System introduced was Decimal, Binary, Octal, and Hexadecimal. Each Number System had their corresponding base and coefficients which is shown below:

    Number System           Base              Coefficients

  • Decimal                   10                      0-9
  • Binary                       2                       0, 1
  • Octal                         8                       0-7
  • Hexadecimal            16                    0-9, A-F
The Base Conversion was also discussed and as follows:
  1. Base-r to Decimal
  2. Decimal to Base-r
  3. Binary to Octal
  4. Binary to Hexadecimal
  5. Octal to Binary
  6. Hexadecimal to Binary
  7. Octal to Hexadecimal or Hexadecimal to Octal
Each Base conversion has its procedures and it has also a trick so that you can able to convert it faster. The Base-r to Decimal trick was just to align the numbers to 1,2,4,8,16,32,64,128 and so on and each aligned numbers at 1 will be added and the sum would be the answer but this is just for base 2 numbers. 
The Decimal to Base-r was the process of division and you will divide it by r in list view and accumulate its remainders and read the remainders up and that would be the answer. 
The Binary to Octal was to partition the binary numbers into groups of 3 and you can now compute its equivalent in decimal and that would be the answer. 
The Binary to Hexadecimal was to partition the binary number into groups of 4 and just like the Binary to Octal compute the equivalent decimals and that would be the answer. 
The Octal to Binary was to convert the 3 digits to its binary equivalent. 
The Hexadecimal to Binary was to convert each hexadecimal digit to its 4 digit binary equivalent. The Octal to Hexadecimal or Hexadecimal to Octal was to convert it first to either Binary or Decimal then you may convert it to octal or hexadecimal.   

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