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# 5.2 Numbering systems

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### 5.2 Numbering systems

1. 1. Module 5: Digital Techniques and Electronic Instrument Systems 5.2 Numbering Systems
2. 2. Number and Base  Base: How many symbols (digits) are used in the current numbering system?  e.g. if the base of a number is 10, we use (maximum) 10 symbols to display this number.  if the base of a number is 8, we use 8 symbols to display this number. (0, 1, 2, 3, 4, 5, 6, 7).  Examples: 1578, 1808210, 1001012.
3. 3. MSD and LSD  In every numbering system, the value of a digit is determined not only by its symbol, but also by its position.  The first digit of a number is called Most Significant digit (MSD).  The last digit of a number is called Less Significant digit (LSD).  Example: 184470287 MSD LSD
4. 4. Binary System Rules  0 + 0 = 0  1 + 0 = 1  0 + 1 = 1  1 + 1 = 0 and 1 carry.  0 – 0 = 0  1 – 0 = 1  0 – 1 = 1 with 1 carry  1 – 1 = 0  Complementary subtraction:  Get the complementary of the subtrahend.  Add 1  Make addition  Discard any carries that exceed the size of the minuend.
5. 5. Numbering System Conversions  Decimal to digital:  I divide the decimal number by 2  I repeatedly divide the result by 2, until the dividend becomes zero.  The residue of each division in reverse order is the binary number.  Digital to decimal:  In the first digit d0 of the binary number I assign d0 *20.  In the nth digit of the binary number I assign dn *2n.  The sum: d0*20+ d1*21 + … + dn*2n is the decimal number.  Octal, Hex number conversion:  The same methodology, but “2” is replaced with “8” and “16” respectively.