![]() ![]() Why is it called “floating point”?Īs the name suggests, the point (decimal point) can float. Depending on the use, there are different sizes of binary floating point numbers. A binary floating point number is a compromise between precision and range. ![]() It would need an infinite number of bits to represent this number. Imagine the number PI 3.14159265… which never ends. However, floating point is only a way to approximate a real number. This is where floating point numbers are used. To represent all real numbers in binary form, many more bits and a well defined format is needed. ![]() However, this only includes whole numbers and no real numbers (e.g. in binary.A binary number with 8 bits (1 byte) can represent a decimal value in the range from 0 – 255. In your question you said that 1/10 in decimal equals 1/1010 in binary.1 (1/10) in decimal actually equals 0.0 00110011 00110011. ĭecimal 1/10 converts to an infinite binary fraction. We are finished in Step 3, because we had 0 as the fractional part of our result there. Step 4: In fact, we do not need a Step 4. 50 x 2 = 1.00, the third binary digit to the right of the point is a 1. The whole number part of the result is now the next binary digit to the right of the point. 50 so there actually is no whole number part to disregard in this case), we multiply by 2 once again. Step 3: Disregarding the whole number part of the previous result (this result was. 25 x 2 = 0.50, the second binary digit to the right of the point is a 0. We will continue this process until we get a zero as our decimal part or until we recognize an infinite repeating pattern. The whole number part of this new result is the second binary digit to the right of the point. ![]() Step 2: Next we disregard the whole number part of the previous result (the 1 in this case) and multiply by 2 once again. 625 x 2 = 1.25, the first binary digit to the right of the point is a 1. The whole number part of the result is the first binary digit to the right of the point. Step 1: Begin with the decimal fraction and multiply by 2. Let's take a look at converting the decimal value of 0.625 to binary. ![]()
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