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Math Help - Binary question

  1. #1
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    Binary question

    1) How do you get 1427 as a binary number? I know the answer but i'm struggling how to WORK the answer out. Would be good if someone told me how to work it out

    2) 00110111
    +00010111
    = 001001100

    How do i work out the row of carries?

    Thanks
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  2. #2
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    1) I'll write a / b = (x, y) to mean that a divided by b gives the integer ratio x and the remainder y. E.g., 12 / 3 = (3, 0) and 7 / 3 = (2, 1).

    So...

    1427 / 2 = (713, 1)
    713 / 2 = (356, 1)
    356 / 2 = (178, 0)

    (Several lines skipped)

    11 / 2 = (5, 1)
    5 / 2 = (2, 1)
    2 / 2 = (1, 0)
    1 / 2 = (0, 1)

    You stop when the integer ratio is 0. Now read the remainders up. The result is 1011...011.

    2) This is pretty similar to addition to the base 10. You mark the column to the left of the current one as having a carry if the current column adds to 2 or more (including the carry for the current column). I got the row of carries to be 01101110.
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  3. #3
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    Thanks man.

    I have another question.

    when 110010110011011001101001100111 is converted to an eight digit hexadecimal number, what is the position of the digit 3? count the positions starting from 1 on the left.

    Could you please tell me how to do this. Thx
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  4. #4
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    When you convert from binary to hexadecimal, you break the number into groups of four digits (because 16 = 2^4) starting from the right. So this would be 0011 0010 1100 1101 1001 1010 0110 0111 if you add two zeros up front to make the first group contain 4 digits. Now each group can be converted independently. Since 3 is 0011, the answer is 1.
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  5. #5
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