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Number Systems, Base Conversions, and Computer Data ...

Number Systems, Base Conversions, and Computer Data Representation Decimal and Binary Numbers When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate power of 10 depending on its position in the Number : For example: 843 = 8 x 102 + 4 x 101 + 3 x 100 = 8 x 100 + 4 x 10 + 3 x 1 = 800 + 40 + 3 For whole numbers, the rightmost digit position is the one s position (100 = 1). The numeral in that position indicates how many ones are present in the Number . The next position to the left is ten s, then hundred s, thousand s, and so on. Each digit position has a weight that is ten times the weight of the position to its right. In the decimal Number system, there are ten possible values that can appear in each digit position, and so there are ten numerals required to represent the quantity in each digit position.

Another example: The same number in unpacked BCD (requires 32 bits) 00000101 00000110 00001001 00000011 5 6 9 3 The use of BCD to represent numbers isn’t as common as binary in most computer systems, as it is not as space efficient. In packed BCD, only 10 of the 16 possible bit patterns in each 4 bit unit are used.

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