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    Converting from Binary to Decimal

    "There are 10 types of people in this world. Those who do understand binary and those who don't."

    If the quote above doesn't make sense to you...then I'm sorry to say that you're one of the people who don't undersand binay numbers. At the very least, you don't yet undersand how to read binary numbers. Hopefully, by the end of this web page the quote will make sense!

    How to convert a decimal number to its binary equivalent

    Convert 9 to binary.
         

    Determine the largest power of 2 that is smaller than the decimal number. 

    23 = 8

     
    The power 3 means that we go 4 bits (start counting at 20)   XXXX  (4 digits)
    Divide that largest power into the decimal and find its remainder 1XXX
    Take the remainder and divide that by the next lowest power of 2 or 2or the process with the remainder   10XX
    Repeat  with 21

    100X

    Repeat  with 20

    1001


    Example 2 of how Convert Decimal to binary

    In this example, we will practice converting 31 to its binary equivalent
    1) What is the largest power of 2 that goes into 31?
    Answer
    24 = 16
    2) From this, we know that there will be how many digits in our binary number
    Answer
    There will be five digits.
    4 +1 = 5
    4) Divide 31 by 16
    Answer


    1XXXX
    5) Now, determine how many times 23 goes into 15.
    Answer

    11XXX
    6) Determine how many times, 22 goes into 7
    Answer


    111XX
    7) Determine how many times, 21 goes into 3
    Answer


    1111X
    8) Determine howmany times, 20 goes into 1
    Answer


    111112 is the solution and is the same as 3110
    Now, let's revisit the binary number joke.

    "There are 10 types of people in this world. Those who do understand binary and those who don't."

    Hopefully, you get the joke now. "10 types" is really "102 types" since the "10" is really a binary number. If you convert 102 from binary to decimal...you have the number 2 in base 10!

    Practice converting decimal and binary numbers with this free online calculator.
    Convert from Binary to Decimal
    Try going in the other direction: from binary to decimal
    Convert 111001111012 from binary to decimal.
    Answer

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