document.write( "Question 764867: Convert the number to a numeral in base 10.
\n" ); document.write( "1100 two=? \n" ); document.write( "
Algebra.Com's Answer #465783 by ramkikk66(644)\"\" \"About 
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document.write( "The number given is 1100 to the base 2 (which is in the \"binary\" system). \r\n" );
document.write( "We have to convert to base 10, which is the \"decimal\" system.\r\n" );
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document.write( "If you understand how the decimal system works, it is not difficult to understand\r\n" );
document.write( "binary.\r\n" );
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document.write( "In the decimal system, the unit's place has a value of 10^0 or 1, the 10's place\r\n" );
document.write( "has a value 10^1 or 10, 100's place has a value 10^2 or 100 and so on.\r\n" );
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document.write( "So to get the value of a number in the decimal system, you multiply the unit's \r\n" );
document.write( "place by 1 (or 10^0), 10's place by 10 (or 10^1), 100's place by 10^2 etc.\r\n" );
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document.write( "e.g. the number 1234 is actually (starting from the rightmost, unit's place,\r\n" );
document.write( "and moving left, one digit at a time)\r\n" );
document.write( "4*10^0 = 4 *1 = 4 +\r\n" );
document.write( "3*10^1 = 3 *10 = 30 +\r\n" );
document.write( "2*10^2 = 2 * 100 = 200 +\r\n" );
document.write( "1*10^3 = 1 * 1000 = 1000 = 1000 + 200 + 30 + 4 = 1234.\r\n" );
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document.write( "Similarly, in the binary system each element is called a \"bit\" - 1 or 0.\r\n" );
document.write( "(Just as a digit in the decimal system can have only 10 possible values 0 \r\n" );
document.write( "to 9, a \"bit\" in binary can have only 2 possible values - 0 or 1.\r\n" );
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document.write( "It is in base 2 (instead of 10), which means the rightmost bit has a value\r\n" );
document.write( "of 2^0, the next has a value of 2^1 = 2, the next has a value of 2^2 = 4 and\r\n" );
document.write( "so on.\r\n" );
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document.write( "So to convert 1100, we do the multiplication as follows (starting from right,\r\n" );
document.write( "and moving left, one bit at a time)\r\n" );
document.write( "0*2^0 = 0*1 = 0 +\r\n" );
document.write( "0*2^1 = 0*2 = 0 +\r\n" );
document.write( "1*2^2 = 1*4 = 4 +\r\n" );
document.write( "1*2^3 = 1*8 = 8 = 0 + 0 + 4 + 8 = 12.\r\n" );
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document.write( "The binary number 1100 (base 2) has a value of \"highlight%2812%29\" in base 10.\r\n" );
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document.write( "Hope this helps :) Let me know if it is not clear.\r\n" );
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