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Q&A #9409

Teachers' Lounge Discussion: Solving algebraic equations

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2003030518:05:34
Subject: Re: math; base 16 to base 10

On 2003030515:24:44, Tammy Amero wrote:
>	
>I need some help with a math question that my two girls are doing.
The
>question is base 10 to base16 how do you do that
>
There 16 single digit numerals in base 16.

0,1,2,3,4,5,6,7,8,9,   a,   b,  c,  d,   e,    f 
0,1,2,3,4,5,6,7,8,.9,10,11,12,13, 14,15

Remember that in base 10, we have ones, tens, hundreds, thousands etc.
In base 16 you have ones, sixteens, 256's, 4096's etc.  

Lets convert 161 base 10 to base 16.  
Make a place value table like this and convert 161 to base 16.  We can
expess 160 as 10 times 16 with one left over.  So, there the
hexadecimal number is a1 since a stands for 10 and the one left over
goes in the ones column.  I will do a bunch of numbers:

b^3        b^2       b^1         b^0
16^3      16^2      16^1      16^0
4096     256's      16's         1's
----------------------------------------
                    a            1  = 10x16 + 1       = 161 base 10 
           1        1            1  = 256 + 16 + 1 = 273  base 10
           2        2            2  = 2x256 + 2x16 + 2x1 = 546 base 10
           a        b            c  = 10x 256+11x16+12x  = 2748

since 10=a, 11=b, 12=c


So, if you wanted to convert 2748 base 10 to base 16, you would divide
by 256 is see how many 256's are in 2748.  There are 10 and then you
would see how many 16's are in the remainder (2748-2560) and you see
that there are 11 16's and 12 ones left.  Not too hard, but a
scientific calculator would help.  My HP6s converts to decimal
,binary, octal, and hexadecimal. Abc hex = 2748 dec

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