document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190037>Question 1190037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert the following decimal numbers to into binary format\r<BR>\n" );
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document.write( "a. 15\r<BR>\n" );
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document.write( "b. 210\r<BR>\n" );
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document.write( "c. 119\r<BR>\n" );
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document.write( "Can you please explain me this homework question step-by-step? Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821585 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The other tutors have great answers. Here's an alternative approach\r<BR>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "We'll need the powers of 2<BR>\n" );
document.write( "1,2,4,8,16,32,...\r<BR>\n" );
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document.write( "Start with 15. Then subtract off the largest possible power of 2. In this case, we can subtract off 8<BR>\n" );
document.write( "15-8 = 7<BR>\n" );
document.write( "Then subtract off 4<BR>\n" );
document.write( "7-4 = 3<BR>\n" );
document.write( "Subtract off 2<BR>\n" );
document.write( "3-2 = 1<BR>\n" );
document.write( "Then subtract off 1<BR>\n" );
document.write( "1-1 = 0\r<BR>\n" );
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document.write( "Work that process in reverse and we get<BR>\n" );
document.write( "15 = 1+2+4+8<BR>\n" );
document.write( "Showing that<BR>\n" );
document.write( "15 base 10 = <font color=red>1111 base 2</font><BR>\n" );
document.write( "Each '1' is like a lightswitch that turns on the powers of 2 we're summing. \r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "We could use the previous idea but here's another way\r<BR>\n" );
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document.write( "15 base 10 = 1111 base 2<BR>\n" );
document.write( "2 base 10 = 0010 base 2\r<BR>\n" );
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document.write( "13 base 10 = (15 base 10) - (2 base 10)<BR>\n" );
document.write( "13 base 10 = (1111 base 2) - (0010 base 10)<BR>\n" );
document.write( "13 base 10 = 1101 base 2\r<BR>\n" );
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document.write( "210 base 10 = 208 base 10 + 2 base 10<BR>\n" );
document.write( "210 base 10 = (16*13) base 10 + 2 base 10<BR>\n" );
document.write( "210 base 10 = 1101 0000 base 2 + 10 base 2 ... see note below<BR>\n" );
document.write( "210 base 10 = <font color=red>1101 0010 base 2</font>\r<BR>\n" );
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document.write( "note: multiplying by 16 in base 2 is as easy as sticking four zeros at the far right end of the number<BR>\n" );
document.write( "It's not a coincidence that 2^4 = 16.\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Like with part (b), I'll try to break this number into parts of 16. Or at least, try to get close to such multiples of 16.\r<BR>\n" );
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document.write( "As Alan alluded to, it's probably better to work with hexadecimal (base 16) since the numbers in binary are very long strings of 1's and 0's. It's easy to get lost.\r<BR>\n" );
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document.write( "7 base 10 = 0111 base 2\r<BR>\n" );
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document.write( "119 base 10 = 112 base 10 + 7 base 10<BR>\n" );
document.write( "119 base 10 = (16*7) base 10 + 7 base 10<BR>\n" );
document.write( "119 base 10 = 0111 0000 base 2 + 0111 base 2<BR>\n" );
document.write( "119 base 10 = <font color=red>0111 0111 base 2</font>\r<BR>\n" );
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document.write( "If you are more familiar with the other methods presented by the other tutors, then ignore my post entirely. \r<BR>\n" );
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document.write( "I recommend the use of any online calculators that quickly convert from binary to decimal (and vice versa) to check your work. Keep in mind that it's not a good idea to rely entirely on the calculator because your teacher will want you to show your work (or thought process). The calculator is merely a tool to see if you have the right answer or not.<BR>\n" );
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