![]() ![]() Then, move it left by as many positions as you have done multiplying in step 2 and 3. Imagine, the binary point is on the most right (after last binary digit). The binary representation of the integer number is shown. Switch to programmer's mode and enter value received after step 3, rounded to integer (unfortunately, that is not done automatically when switching mode, at least in Windows 10's Calculator app). IMPORTANT! Remember, how many times you multiplied initial value by 2 (in step 2 and repeated 3). Repeat step 2 (pressing = key alone, again and again), until you receive number which is integer - or very close to integer (see remark below). In standard mode enter a decimal number (can be fractional) to convert, e.g. A workaround to achieve your goal is like this: Unfortunatelly, windows calculator in programmer's mode operate on integer values only. But remember: not all decimal fractions can be represented in binary form exactly - some rounding must be applied then, especially if only limited count of bits can be used (which is always true in real computer science world). In fact, that is how real/double numbers are represented in computers (although usually binary point position is stored, instead of the "point character"). If you really felt like it, you could use a memory viewing tool and spy on values as you type them in the calculator, but again, that is a different topic.Ĭheck out to have an idea of how the floating point numbers are stored and Generally, fraction value CAN be represented in binary, using kind of "binary point" (counterpart of decimal point). Now, to answer your question, while Windows calculator stores the numbers in this form, it hasn't been designed to show you the intermediate/raw values in the memory. Your number 0.21 is stored in memory as 1.6799999475479126 * 2^(-3) which is equivalent to 0.20999999344348907470703125 (windows calculator shows this as 0.209999993443489075 when calculating manually)Īny calculator that utilises this standard will store numbers in the same format (if it doesn't, excluding different endianness, it probably has a different way of storing floating point numbers, so when passing values from one piece of software/hardware to another, translation must happen, but this is a different topic altogether). Think of this as a scientific notation, which is a * 10^b, where a must be [1, 10) (meaning from 1.0 up to, but not including 10, e.g. So the way fractions are represented in memory is according to the IEEE-754 standard for floating point numbers.Ī number as simple as decimal 123 when stored as floating point number (e.g.
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