document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190115>Question 1190115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert the following unsigned 8 bit binary numbers into both hex and decimal \r<BR>\n" );
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document.write( "a. 00110110 base 2\r<BR>\n" );
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document.write( "b. 00111101 base 2\r<BR>\n" );
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document.write( "c. 01111100 base 2\r<BR>\n" );
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document.write( "Can you please explain 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 #821680 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=821680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll go over part (a) to get you started.\r<BR>\n" );
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document.write( "Let's convert this base 2 value<BR>\n" );
document.write( "0011 0110 <BR>\n" );
document.write( "into base 10, aka decimal\r<BR>\n" );
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document.write( "To start off, we'll just focus on the last set of four values 0110\r<BR>\n" );
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document.write( "Any four digit number like this has the template of<BR>\n" );
document.write( "abcd base 2 = (a*2^3 + b*2^2 + c*2^1 + d*2^0) base 10<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "0110 base 2 = (0*2^3 + 1*2^2 + 1*2^1 + 0*2^0) base 10<BR>\n" );
document.write( "0110 base 2 = 6 base 10<BR>\n" );
document.write( "Effectively it's like saying<BR>\n" );
document.write( "0110 base 2 = 2^2+2 base 10 = 4+2 base 10 = 6 base 10\r<BR>\n" );
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document.write( "The middle '1's are switches that flip on to add the 2^2 and 2^1 terms. The 0s mean we don't add those other powers of 2.\r<BR>\n" );
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document.write( "Through similar steps we will have<BR>\n" );
document.write( "0011 base 2 = 3 base 10\r<BR>\n" );
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document.write( "Now if we were to multiply by 16, then that's the same as tacking four 0's at the end of the binary number (this works because 2^4 = 16)<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "0011 0000 base 2 = (3 base 10)*(16 base 10)<BR>\n" );
document.write( "0011 0000 base 2 = 48 base 10\r<BR>\n" );
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document.write( "Lastly,<BR>\n" );
document.write( "(0011 0000 base 2) + (0110 base 2) = (48 base 10) + (6 base 10)<BR>\n" );
document.write( "0011 0110 base 2 = <font color=red>54 base 10</font>\r<BR>\n" );
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document.write( "You can use a calculator like this<BR>\n" );
document.write( "https://www.binaryhexconverter.com/binary-to-decimal-converter<BR>\n" );
document.write( "to help confirm the answer\r<BR>\n" );
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document.write( "---------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "The hexadecimal numbering system goes from 0 to F<BR>\n" );
document.write( "The 0 to 9 work the same in base 10<BR>\n" );
document.write( "The A through F are the 6 extra values to get 10+6 = 16 items total\r<BR>\n" );
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document.write( "A base 16 = 10 base 10<BR>\n" );
document.write( "B base 16 = 11 base 10<BR>\n" );
document.write( "C base 16 = 12 base 10<BR>\n" );
document.write( "D base 16 = 13 base 10<BR>\n" );
document.write( "E base 16 = 14 base 10<BR>\n" );
document.write( "F base 16 = 15 base 10\r<BR>\n" );
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document.write( "Once we reach number F, the next number is 10<BR>\n" );
document.write( "F base 16 = 15 base 10<BR>\n" );
document.write( "10 base 16 = 16 base 10<BR>\n" );
document.write( "11 base 16 = 17 base 10<BR>\n" );
document.write( "12 base 16 = 18 base 10<BR>\n" );
document.write( "and so on\r<BR>\n" );
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document.write( "Notice that once we reach the end of the digits in our base 16 system, we add on another slot and reset things back to zero so to speak. \r<BR>\n" );
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document.write( "Hopefully this helps clear up any confusion of how the hexadecimal system works. \r<BR>\n" );
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document.write( "Anyways, let's convert the binary number 0011 0110 to hexadecimal\r<BR>\n" );
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document.write( "0011 base 2 = 3 base 10<BR>\n" );
document.write( "0110 base 2 = 6 base 10<BR>\n" );
document.write( "Since both values (3 and 6) are smaller than 10, this means we won't use letters A through F.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "0011 0110 base 2 = <font color=red>36 base 16</font>\r<BR>\n" );
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document.write( "Here's a free calculator to help check your work<BR>\n" );
document.write( "https://www.binaryhexconverter.com/binary-to-hex-converter<BR>\n" );
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