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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 .

In unpacked BCD, only 10 of the 256 possible bit patterns in each byte are used. A 16 bit quantity can represent the range 0-65535 in binary, 0-9999 in packed BCD and only 0-99 in unpacked BCD. Fixed Precision and Overflow. So far, in talking about binary numbers, we haven’t considered the maximum size of the number.

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