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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)

```

```
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

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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