• Maths index

    Binary Arithmetic

    If I gave you a red ball and a blue ball and asked you to do arithmetic with them using one colour for one number and the other for another number (no other numbers allowed) I would be asking you to do binary arithmetic.

    Binary is from the Latin binarius, which means doing it with two together (bini + ary)

    At first sight, it may seem that you cannot count higher than two. But this is not so. In our normal counting we have only ten digits (0 to 9), but, by putting them in different places, we can carry on counting until we stop with exhaustion. We can do the same with two balls.

    The blue ball on its own is 0
    The red ball on its own is 1
    The red ball followed by the blue ball is 2
    Two red balls is three
    The red ball followed by two blue balls is four
    The red ball, a blue ball, then a red ball is five
    Two red balls then a blue ball is six
    Three red balls is seven
    The red ball followed by three blue balls is eight
    The red ball, two blue balls, then a red ball is nine
    A red ball, a blue ball, a red ball, then a blue ball is ten
    A red ball, a blue ball, then two red balls is eleven
    Two red balls and two blue balls is twelve
    Two red balls, a blue ball, then a red ball is thirteen
    Three red balls, then a blue ball is fourteen
    Four red balls is fifteen

    We can make Binary numbers by writing 0 for the blue ball and 1 for the red balls.

    In binary numbers:

    0 means 0
    1 means 1
    10 means two
    11 means three
    100 means four
    101 means five
    110 means six
    111 means seven
    1000 means eight
    1001 means nine
    1010 means ten
    1011 means eleven
    1100 means twelve
    1101 means thirteen
    1110 means fourteen
    1111 means fifteen
    There are 10 types of people in the world -

    Those who understand binary and

    Those who do not

    When you understand that joke you understand binary

    Click here for an electronic calculator that converts our normal numbers to binary numbers

    If all this driven you crazy, then pity the computer you are reading this on. Computers do all their counting in binary arithmetic. In fact, they do everything in binary. When you move the scroll bar the command is converted into binary patterns for the computer to understand it.

    If you enjoy binary arithmetic and you can do it very very fast, perhaps you should apply for a job as a computer.

    Click here for more about thinking like a computer.

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