How to Convert From Base-10 to Binary
People have developed a base-10 counting system--one that includes the numbers zero through nine--likely for the simple reason that humans have 10 fingers to count on. Computers, however, only understand on or off, so at their most basic level, they function in the binary system. The binary system uses only the digits zero and one when counting. You can convert any base-10 number to its corresponding binary equivalent using a mathematical process.
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Instructions
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Write down "1" in the leftmost empty spot for your binary number if the base-10 number you are converting is odd, and "0" if it is even. To convert the base-10 number seven to binary, for example, you would write down "1" as your first step, since the leftmost empty spot when beginning is simply the first digit of the binary number.
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Subtract one from your base-10 number if it is odd, otherwise do nothing. You would subtract one from seven to get six.
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Divide your base-10 number (if it is even) or your base-10 number minus one (if it is odd) by two. In the example, you would divide (7 - 1)/2 to get 6/2 = 3.
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Go back to the first step and repeat it, using the product of the division you just did as your new base-10 number. As directed in the first step, you would then enter either a "1" or a "0" in subsequent spots of your binary number, moving to the left each time. You would continue this until you get a base-10 number of zero, at which point the series of ones and zeros you have written down will be the binary number corresponding to your original base-10 number. In the example of seven, your "new" base-10 number would be three, which is odd, so you write "1" to the left of the "1" you already have, to obtain "11." You subtract one and divide by two to get (3-1)/2 = 1, which is your next number. This is odd, so you write "1" and get "111." Subtracting one gives you zero, so you are finished. The binary representation of seven is "111."
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Tips & Warnings
There are other number systems in addition to base-10 and binary, such as the octal system, which is base-8.
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