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All About The Numbers: Sixteen

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

  • This is how it is represented in octal:
    20
    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:
    2*8+0=16
    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

  • How to Add with The Number 16
    n + 16 = ?

    Let's add 16 to a number and see what we get!

    0 + 16 = 16 0 +        
               		 =        
           
    1 + 16 = 17 +        
               		 =         
           
    2 + 16 = 18 +        
               		 =         
            
    3 + 16 = 19 +        
               		 =          
            
    4 + 16 = 20 +        
               		 =          
             
    5 + 16 = 21 +        
               		 =           
             
    6 + 16 = 22 +        
               		 =           
              
    7 + 16 = 23 +        
               		 =            
              
    8 + 16 = 24 +        
               		 =            
               
    9 + 16 = 25 +        
               		 =             
               
    10 + 16 = 26 +        
               		 =             
                

  • How to Add with The Number 20 in Octal
    n + 20 = ?

    Let's add 20 in Octal to a number and see what we get!

    0 + 20 = 20
    1 + 20 = 21
    2 + 20 = 22
    3 + 20 = 23
    4 + 20 = 24
    5 + 20 = 25
    6 + 20 = 26
    7 + 20 = 27
    10 + 20 = 30
    11 + 20 = 31
    12 + 20 = 32

  • How to Subtract with The Number 16
    n - 16 = ?

    Let's subtract 16 from a number and see what we get!

    16 - 16 = 0        
               		 -        
               		 = 0
    17 - 16 = 1         
               		 -        
               		 =
    18 - 16 = 2         
                		 -        
               		 =
    19 - 16 = 3          
                		 -        
               		 =
    20 - 16 = 4          
                 		 -        
               		 =
    21 - 16 = 5           
                 		 -        
               		 =
    22 - 16 = 6           
                  		 -        
               		 =
    23 - 16 = 7            
                  		 -        
               		 =
    24 - 16 = 8            
                   		 -        
               		 =
    25 - 16 = 9             
                   		 -        
               		 =
    26 - 16 = 10             
                    		 -        
               		 =

  • How to Multiply with The Number 16
    n * 16 = ?

    Let's multiply 16 to a number and see what we get!

    0 * 16 = 0
    1 * 16 = 16
    2 * 16 = 32
    3 * 16 = 48
    4 * 16 = 64
    5 * 16 = 80
    6 * 16 = 96
    7 * 16 = 112
    8 * 16 = 128
    9 * 16 = 144
    10 * 16 = 160
    11 * 16 = 176
    12 * 16 = 192
    13 * 16 = 208
    14 * 16 = 224
    15 * 16 = 240
    16 * 16 = 256

    x16=
    x1=16
    x2=32
    x3=48
    x4=64
    x5=80
    x6=96
    x7=112
    x8=128
    x9=144
    x10=160

  • How to Divide with The Number 16
    n / 16 = ?

    Let's divide 16 from a number and see what we get!

    160 / 16 = 10
    144 / 16 = 9
    128 / 16 = 8
    112 / 16 = 7
    96 / 16 = 6
    80 / 16 = 5
    64 / 16 = 4
    48 / 16 = 3
    32 / 16 = 2
    16 / 16 = 1
    0 / 16 = 0

  • How to Exponent with The Number 16 as a power
    n ^ 16 = ?

    Let's raise a number to the power of 16 and see what we get!

    0 ^ 16 = 0; 0 raised to any nozero positive number is 0; it's the same as 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0.
    1 ^ 16 = 1; 1 raised to any power is 1; it's the same as 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1.
    2 ^ 16 = 65,536; it's the same as 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.
    3 ^ 16 = 43,046,721; it's the same as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.
    4 ^ 16 = 4,294,967,296; it's the same as 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4.
    5 ^ 16 = 152,587,890,625; it's the same as 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5.
    6 ^ 16 = 2,821,109,907,456; it's the same as 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6.
    7 ^ 16 = 33,232,930,569,601; it's the same as 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7.
    8 ^ 16 = 281,474,976,710,656; it's the same as 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8.
    9 ^ 16 = 1.85302018885184E+15; it's the same as 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9.
    10 ^ 16 = 1E+16; it's the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

  • How to Exponent with The Number 16 as a base
    16 ^ n = ?

    Let's raise 16 to a power and see what we get!

    16 ^ 0 = 1; a nonzero number raised to zero is 1.
    16 ^ 1 = 16; it's the same as 16.
    16 ^ 2 = 256; it's the same as 16 x 16.
    16 ^ 3 = 4,096; it's the same as 16 x 16 x 16.
    16 ^ 4 = 65,536; it's the same as 16 x 16 x 16 x 16.
    16 ^ 5 = 1,048,576; it's the same as 16 x 16 x 16 x 16 x 16.
    16 ^ 6 = 16,777,216; it's the same as 16 x 16 x 16 x 16 x 16 x 16.
    16 ^ 7 = 268,435,456; it's the same as 16 x 16 x 16 x 16 x 16 x 16 x 16.
    16 ^ 8 = 4,294,967,296; it's the same as 16 x 16 x 16 x 16 x 16 x 16 x 16 x 16.
    16 ^ 9 = 68,719,476,736; it's the same as 16 x 16 x 16 x 16 x 16 x 16 x 16 x 16 x 16.
    16 ^ 10 = 1,099,511,627,776; it's the same as 16 x 16 x 16 x 16 x 16 x 16 x 16 x 16 x 16 x 16.

  • This is how the number 16 it is represented in binary:
    10000
    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, the next one to the left is how many eights there are, or 2^3's there are, and the one on the far left is how many sixteens there are, or 2^4's there are.
    You multiply each of the digits by the place they're slotted like this:
    1*2^4+0*2^3+0*2^2+0*2+0=16

  • How to Add with The Number 10000 in Binary
    n + 10000 = ?

    Let's add 1100 in Binary to a number and see what we get!

    0 + 10000 = 10000
    1 + 10000 = 10001
    10 + 10000 = 10010
    11 + 10000 = 10011
    100 + 10000 = 10100
    101 + 10000 = 10101
    110 + 10000 = 10110
    111 + 10000 = 10111
    1000 + 10000 = 11000
    1001 + 10000 = 11001
    1010 + 10000 = 11010
    1011 + 10000 = 11011
    1100 + 10000 = 11100
    1101 + 10000 = 11101
    1110 + 10000 = 11110
    1111 + 10000 = 11111

    Remember, just like in a computer, there are only zeros and ones, nothing else.

  • This is how it is represented in hex:
    10
    In hex, the letter "A" represents a "10" in decimal, "B" for "11", "C" for "12", "D" for "13", "E" for "14", and "F" for "15". To translate from hex to decimal, translate each digit to decimal, and pretend that there really is a two-digit number in a hex digit slot. The rightmost digit is how many ones there are, the one just to the left is how many 16s there are. You multiply each of the digits by the place they're slotted like this:
    1*16+0=16

  • How to get the number 16 by adding two digits:

    15+1

    +  


    14+2

    +


    13+3

    +


    12+4

    +


    11+5

    +


    10+6

    +


    9+7

    +


    8+8

    +


    NOTE: You can also reverse the digits 15+1 to get 1+15 and it will still be 16; same with 14+2, 13+3, 12+4, 11+5, 10+6, 9+7, and 8+8; try it yourself and see.

  • How to get the number 16 by subtracting two digits:
    17-1

    -  


    18-2

    -  


    20-4

    -  


    Do you see a pattern developing? If you increase the first part of 17-1 (17) by one and you also do the same with the second part (1), you still get 16. Even if you have gotten up to 2,355,665,496-2,355,665,480 it will still get 16. Go ahead and try it with even higher numbers.

  • How to get the number 16 by multiplying two digits:
    8*2

    x


    Two rows of 8 added together produce 16, because 8*2 is 8 added to itself 2 times like this:
    8+8

    +

    Likewise, 2*8 is also 16 because you are adding eight 2's together like this: 2+2+2+2+2+2+2+2, or like this:

    + + + + + + +


    4*4

    x


    Four rows of 4 added together produce 16, because 4*4 is 4 added to itself 4 times like this:
    4+4+4+4

    + + +

    Likewise, 4*4 is also 16 because you are adding four 4's together like this: 4+4+4+4, or like this:

    + + +

  • How to get the number 16 by dividing two digits:
    32/2

    You originally have 32 balls, and you split it into 2 piles, you get 16 in each pile.


    and

    Now, that is the same as dividing 16 into one pile, as in 16/1=16, but 32/2=16, so is 64/4=16, even 131,072/8,192=16. 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 16/1 fraction so that the ratio is always 16:1, or simply 16.

  • How to get the number 16 by powering two digits:
    4^2

        x    

    The 4 in the 4^2 is the base and the 2 is the exponent, meaning how many bases should be multiplied by each other. Thus, 4^2 can be represented as 4*4, where you multiply the two fours together, you get 16, hence: 4 * 4 = 16.

    Or to break it down even further,
    4*4 = 4+4+4+4 = 16

    If 4^2=16, does 2^4=16 also? Let's see here:

    2^4=2*2*2+2=16

    4^2=4*4=16
    Does 16=16? Yes. Therefore, 4^2=2^4. Normally this does not work, but in this case, it does.

    2^4

      x   x   x  

    The 2 in the 2^4 is the base and the 4 is the exponent, meaning how many bases should be multiplied by each other. Thus, 2^4 can be represented as 2*2*2*2, where you multiply the four twos together, you get 16, hence: 2 * 2 * 2 * 2 = 16.

    Or to break it down even further,
    2 * 2 * 2 * 2
    = (2 + 2) * 2 * 2
    = ((2 + 2) + (2 + 2)) * 2
    = (((2 + 2) + (2 + 2)) + ((2 + 2) + (2 + 2))) = 16

  • How to get the number 16 by rooting two digits:
    256 SQR 2

















    You can see that if you take 256 of something and arrange it so that its contents are a perfect square, you will get exactly 16 rows of 16 colums of balls.

    You can also imagine that you can get 16 if you take the cube root of 4,096. Since this computer cannot display balls in 3-D, you'll have to get that many blocks, and build a base 16 by 16 and stack the blocks 16 high. You'll use exactly 4,096 blocks to build that perfect cube.

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