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LAST UPDATED: 24 Oct, 2022
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The problem of correctly converting between decimal numbers and IEEE single and double precision values and the IEEE halfway-rounded-to-even rule is concerned. Regardless of how accurately a computer performs floating-point operations, if the data to operate on must be initially converted from the decimal -based representation used by humans into the internal ...
https://www.semanticscholar.org/paper/A-Program-for-Testing-IEEE-Decimal%E2%80%93Binary-Paxson/5b060e22e77180435ff6490b47cc322d6f39c5a5For an interactive explanation of how this conversion process works, I made a webapp that basically summarizes this video:https://float-visualizer.surge.shHe
https://www.youtube.com/watch?v=4DfXdJdaNYsThe decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator by the denominator — and if the division doesn’t come out evenly, you can stop after a certain number of decimal places and round off.
How to convert binary to decimal. The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n): decimal = d0×20 + d1×21 + d2×22 + ...
How to Convert a Percent to a Decimal: Converting from a percent to a decimal is done by removing the percent sign % and dividing the value by 100. Example: 15.6% becomes 15.6 / 100 = 0.156 Example: 235% becomes 235 / 100 = 2.35 The shortcut to convert from a percent to a decimal is to move the decimal point 2 places to the left and remove the percent sign.
To convert to scientific notation, start by moving the decimal place in the number until you have a coefficient between 1 and 10; here it is 3.45. The number of places to the left that you had to move the decimal point is the exponent. Here, we had to move the decimal 4 places to the right, so the exponent is -4.
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