Converting Binary to and From DecimalDate: 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/ |
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