Number Systems

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Review the decimal number system. Base (Radix) is 10 - symbols (0,1, . . 9) Digits For Numbers GT 9, add more significant digits in position to the left, e.g. 19>9. Each position we understand to carry a weight. Weights: 2 10 1 10 0 10 1 10 - 2 10 - 3 10 MSD LSD 3 10 - If we were to write 1936.25 using a power series expansion and base 10 arithmetic: 2 1 0 1 2 3 10 * 5 10 * 2 10 * 6 10 * 3 10 * 9 10 * 1 - - + + + + + Number Systems
The binary number system. Base is 2 - symbols (0,1) - Binary Digits (Bits) For Numbers GT 1, add more significant digits in position to the left, e.g. 10>1. Each position carries a weight (using decimal arith ). Weights: 2 2 1 2 0 2 1 2 - 2 2 - 3 2 MSB 3 LSB 2 - If we write 10111.01 using a decimal power series we convert from binary to decimal: 2 1 0 1 2 3 4 2 * 1 2 * 0 2 * 1 2 * 1 2 * 1 2 * 0 2 * 1 - - + + + + + + 25 . 23 25 . 0 * 1 5 . 0 * 0 1 * 1 2 * 1 4 * 1 8 * 0 16 * 1 = + + + + + + Number Systems

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Recall: 1/4 = 0.25,
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