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Converting Binary to and From Decimal


Date: 06/16/99 at 22:23:39
From: Puneet Shroff
Subject: Converting different bases

I just do not understand bases and I need them for school. I don't 
understand problems like this: 76(base 2) = ________ (base 10)

Please help.


Date: 06/17/99 at 08:59:16
From: Doctor Peterson
Subject: Re: Converting different bases

Hi, Puneet.

The first thing you should do is to look at our FAQ on this subject:

 http://mathforum.org/dr.math/faq/faq.bases.html   

There you will find a number of explanations of what bases are and how 
to convert them. One to start with is

 http://mathforum.org/dr.math/problems/ross8.18.98.html   

where I explain the concept. For help in converting binary to decimal, 
look here:

 http://mathforum.org/dr.math/problems/reinhardt12.21.97.html   

I have a trick that makes the work easier, which may not be explained 
in the FAQ. To convert binary to decimal, you just start at the left 
and repeatedly multiply by 2, then add the next digit.


    1001100 (base 2) = ? (base 10)
     \\\\\\\
      \\\\\\+----------------------+
       \\\\\+------------------+    \
        \\\\+--------------+    \    \
         \\\+----------+    \    \    \
          \\+------+    \    \    \    \
           \+--+    \    \    \    \    \
            \   \    \    \    \    \    \
       ((((((1*2+0)*2+0)*2+1)*2+1)*2+0)*2+0) = 76
                  =    =    =    =    =    =
                  2    4    9    19   38   76

To convert decimal to binary, you repeatedly divide by two and take 
the remainder at each step as the binary digits, starting at the 
right.

    76 (base 10) = ? (base 2)

    76/2 = 38 rem 0
    38/2 = 19 rem 0\
    19/2 =  9 rem 1\\
    9/2  =  4 rem 1\\\
    4/2  =  2 rem 0\\\\
    2/2  =  1 rem 0\\\\\
    1/2  =  0 rem 1\\\\\\
                   \\\\\\\
    76 (base 10) =  1001100 (base 2)

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Number Theory

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