document.write( "Question 1172437: evaluate the following in base (2) arithmetic
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Algebra.Com's Answer #797463 by Edwin McCravy(20065) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Here is an alternate approach.  It, of course amounts to the same thing,\r\n" );
document.write( "but it's more like ordinary addition that you learned in early grades.\r\n" );
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document.write( "Learn to count in base (2) this way: 1,10,11,100,101,110,111,1000,...\r\n" );
document.write( "Write the numbers to add in a column the same way you do ordinary base (10)\r\n" );
document.write( "numbers, but leave room between them because you often need to carry more than\r\n" );
document.write( "one digit:\r\n" );
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document.write( "         1  0  1  0\r\n" );
document.write( "      1  1  0  1  1\r\n" );
document.write( "   1  1  1  0  1  1\r\n" );
document.write( "-------------------\r\n" );
document.write( "                \r\n" );
document.write( "Add the right most column, 0+1+1=10, put down the 0 and carry the 1. I'll\r\n" );
document.write( "put all the \"carry\"-numbers in red, and the digits in the answer in blue: \r\n" );
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document.write( "               1\r\n" );
document.write( "         1  0  1  0\r\n" );
document.write( "      1  1  0  1  1\r\n" );
document.write( "   1  1  1  0  1  1\r\n" );
document.write( "-------------------\r\n" );
document.write( "                  0  \r\n" );
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document.write( "Add the 2nd column from the right, 1+1+1+1=100, put down the 0 and carry 10\r\n" );
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document.write( "           10  1\r\n" );
document.write( "         1  0  1  0\r\n" );
document.write( "      1  1  0  1  1\r\n" );
document.write( "   1  1  1  0  1  1\r\n" );
document.write( "-------------------\r\n" );
document.write( "               0  0  \r\n" );
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document.write( "Add the 3rd column from the right, 10+0+0+0=10, put down 0, and carry 1:\r\n" );
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document.write( "         1 10  1\r\n" );
document.write( "         1  0  1  0\r\n" );
document.write( "      1  1  0  1  1\r\n" );
document.write( "   1  1  1  0  1  1\r\n" );
document.write( "-------------------\r\n" );
document.write( "            0  0  0 \r\n" );
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document.write( "Add the 4th column from the right, 1+1+1+1=100, put down 0 and carry 10:\r\n" );
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document.write( "     10  1 10  1\r\n" );
document.write( "         1  0  1  0\r\n" );
document.write( "      1  1  0  1  1\r\n" );
document.write( "   1  1  1  0  1  1\r\n" );
document.write( "--------------------\r\n" );
document.write( "         0  0  0  0 \r\n" );
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document.write( "Add the 5th column from the right, 10+1+1=100, put down 0 and carry 10:\r\n" );
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document.write( "  10 10  1 10  1\r\n" );
document.write( "         1  0  1  0\r\n" );
document.write( "      1  1  0  1  1\r\n" );
document.write( "   1  1  1  0  1  1\r\n" );
document.write( "--------------------\r\n" );
document.write( "      0  0  0  0  0 \r\n" );
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document.write( "Add the 6th column from the right, 10+1=11, put down 1 and carry 1 to a new\r\n" );
document.write( "column on the far left, there is nothing to add, so bring down the 1:\r\n" );
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document.write( " 1 10 10  1 10  1\r\n" );
document.write( "          1  0  1  0\r\n" );
document.write( "       1  1  0  1  1\r\n" );
document.write( "    1  1  1  0  1  1\r\n" );
document.write( "--------------------\r\n" );
document.write( " 1  1  0  0  0  0  0\r\n" );
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document.write( "So the answer is 1100000.\r\n" );
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document.write( "Edwin
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