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D.T.'s Fun With Math-Eight

Facts About The Number Eight
  • This is how much there is:


  • This is how it is represented in octal:
    The one on the left is how many eights there are and the zero on the right is how many ones there are. To get the decimal representation, just multiply the digit in the eights place by eight, and add that to the number of ones in the ones place:
    Remember, there are no 8's or 9's as digits in an octal, or base-8 system.
    Base eight is like base ten ... if you're missing two fingers --- Tom Lehrer from his novelty tune New Math

  • This is how it is represented in binary:
    The rightmost digit is how many ones there are, the one just to the left is how many twos there are, the one just to the left of that is how many fours there are, or 2^2's there are, and the one on the far left is how many eights there are, or 2^3's there are.
    You multiply each of the digits by the place they're slotted like this:
    Remember, just like in a computer, there are only zeros and ones, nothing else.

  • This is how it is represented in hex:
    The first ten numbers of base ten is the same as those of base hex, so see the number ten for how to use it.

  • How to get the number 8 by adding two digits:

    ******* + *


    ****** + **


    ***** + ***


    **** + ****

    NOTE: You can also reverse the digits 7+1 to get 1+7 and it will still be 8; same with 6+2 and 5+3; try it yourself and see.

  • How to get the number 8 by subtracting two digits:

    ******** - *


    ********* - **


    *********** - ****

    Do you see a pattern developing? If you increase the first part of 9-1 (9) by one and you also do the same with the second part (1), you still get 8. Even if you have gotten up to 2,355,665,488-2,355,665,480 it will still get 8. Go ahead and try it with even higher numbers.

  • How to get the number 8 by multiplying two digits:

    **** & ****

    Two rows of 4 added together produce 8, because 4*2 is 4 added to itself twice like this: 4+4. Likewise, 2*4 is also 8 because you are adding four 2's together like this: 2+2+2+2, or like this:

    ** & ** & ** & **

  • How to get the number 8 by dividing two digits:

    ******** / ********

    You originally have 16 balls, and you split it into 2 piles, you get 8 in each pile. Now, that is the same as dividing 8 into one pile, as in 8/1=8, but 16/2=8, so is 32/4=8, even 65,536/8,192=8. How could this be? Simple. The dividend on the left and the divisor in the middle are multiplied by the same factor from the original 8/1 fraction so that the ratio is always 8:1, or simply 8.

  • How to get the number 8 by powering two digits:




    The 2 in the 2^3 is the base and the 3 is the exponent, meaning how many bases should be multiplied by each other. Thus, 2^3 can be represented as 2*2*2, where you multiply the first twos together to get 4, then you multiply that result by the last two to get 8; Hence: (2*2)*2=4*2=8.
    If 2^3=8, does 3^2=8 also? Let's see here:
    Does 8=9? No. Therefore, 2^3<>3^2.

  • How to get the number 8 by rooting two digits:
    64 SQR 2

    You can see that if you take 64 of something and arrange it so that its contents are a perfect square, you will get exactly 8 rows of 8 colums of balls. You can also imagine that you can get 8 if you take the cube root of 512. Since this computer cannot display balls in 3-D, you'll have to get that many blocks, and build a base 8 by 8 and stack the blocks 8 high. You'll use exactly 512 blocks to build that perfect cube.
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