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Mark Pearl

The Decimal & Binary System and Converting between Binary and Decimal

I am assuming that a basic knowledge of binary and decimal notation is known, if you are unfamiliar with it, read up on binary and decimal

  • The decimal system has a base or radix of 10 – this means that each digit in the number is multiplied by 10 raised to a power corresponding to that digits position.
  • The same principles holds for decimal fractions but negative powers of 10 are used
  • A number with both an integer and fractional part has digits raised to both positive and negative powers of 10
  • In the binary system we have only two digits, 1 & 0 to represent numbers
  • To convert from binary to decimal, all that is required is to multiply each binary digit by the appropriate power of 2 and add the results
  • To convert from decimal to binary, the integer and fractional parts are handled separately

Hexadecimal Notation

  • Because of the inherent binary nature of digital computer components, all forms of data within computers are represented by various binary codes, however the binary system is cumbersome for human beings, thus we use a more compact notation called hexadecimal.
  • Binary digits are grouped into sets of four, each possible combination of four binary digits is given a symbol as follows
0000 = 0 0100 = 4 1000 = 8 1100 = C
0001 = 1 0101 = 5 1001 = 9 1101 = D
0010 = 2 0110 = 6 1010 = A 1110 = E
0011 = 3 0111 = 7 1011 = B 1111 = F

 

  • A sequence of hexadecimal digits can be thought of as representing an integer in base 16, thus 2C = (2H * 16^1) + (CH * 16^0) = (2 * 16^1) + (12 x 16^0) = 44
  • Hexadecimal notation is used not only to represent integers, it is also used as a concise notation for representing any sequence of binary digits
Decimal Binary Hex
0 0000 0
5 0011 5
15 1111 F
16 0001 0000 10
31 0001 0000 1F
255 1111 0000 FF
256 0001 0000 0000 100

 

Benefits of using hexadecimal include

  1. It is more compact than binary notation
  2. In most computers, binary data occupy some multiple of 4 bits, and hence some multiple of a single hexadecimal digit
  3. It is extremely easy to convert between binary and hexadecimal
Posted on Monday, January 30, 2012 6:35 AM | Back to top


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