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 #821572 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I'll do the second example, showing two different ways.<br><BR>\n" );
document.write( "Place values, base 10:<BR>\n" );
document.write( "      1 = 10^0<BR>\n" );
document.write( "     10 = 10^1<BR>\n" );
document.write( "    100 = 10^2<BR>\n" );
document.write( "   1000 = 10^3<BR>\n" );
document.write( "  10000 = 10^4<BR>\n" );
document.write( "   etc.<br><BR>\n" );
document.write( "Place values, base 2:<BR>\n" );
document.write( "           1(base 2) =   1 = 2^0<BR>\n" );
document.write( "          10(base 2) =   2 = 2^1<BR>\n" );
document.write( "         100(base 2) =   4 = 2^2<BR>\n" );
document.write( "        1000(base 2) =   8 = 2^3<BR>\n" );
document.write( "       10000(base 2) =  16 = 2^4<BR>\n" );
document.write( "      100000(base 2) =  32 = 2^5<BR>\n" );
document.write( "     1000000(base 2) =  64 = 2^6<BR>\n" );
document.write( "    10000000(base 2) = 128 = 2^7<BR>\n" );
document.write( "   100000000(base 2) = 256 = 2^8<BR>\n" );
document.write( "   etc.<br><BR>\n" );
document.write( "You should understand how to convert from base 10 to base 2 using place values, because it helps you understand numbers in different bases.  But it is a slow and inefficient process.<br><BR>\n" );
document.write( "Here is how to convert 210 (base 10) to base 2 using place values.<br><BR>\n" );
document.write( "The largest power of 2 less than 210 is 128, which is 10000000 (base 2); the number that remains is 210-128=82<BR>\n" );
document.write( "The largest power of 2 less than 82 is 64, which is 1000000 (base 2); the partially converted number is 10000000+1000000 = 11000000; the number that remains is 82-64=18<BR>\n" );
document.write( "The largest power of 2 less than 18 is 16, which is 10000 (base 2); the partially converted number is 11000000 + 10000 = 11010000; the number that remains is 18-16=2<BR>\n" );
document.write( "2 is 10 in base 2<br><BR>\n" );
document.write( "The conversion is 210 (base 10) = 11010000+10 = 11010010 (base 2).<br><BR>\n" );
document.write( "The process involves repeated subtraction and then repeated referral to a list of powers of 2; that makes the process slow.<br><BR>\n" );
document.write( "Here is a far more efficient way to perform the same conversion.<br><BR>\n" );
document.write( "210/2 = 105 remainder 0<BR>\n" );
document.write( "105 = 52 remainder 1<BR>\n" );
document.write( "52 = 26 remainder 0<BR>\n" );
document.write( "26 = 13 remainder 0<BR>\n" );
document.write( "13 = 6 remainder 1<BR>\n" );
document.write( "6 = 3 remainder 0<BR>\n" );
document.write( "3 = 1 remainder 1<BR>\n" );
document.write( "1 = 0 remainder 1<br><BR>\n" );
document.write( "The converted number in base 2 is the remainders, written in reverse order: 11010010.<br><BR>\n" );
document.write( "That is a much more efficient process.<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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