document.write( "Question 979038: I have work for this question but i couldn't get the proper answer, please help me solve it.
\n" ); document.write( "Multiply 11321*12 base 4 \n" ); document.write( "
Algebra.Com's Answer #600374 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
Base 4 arithmetic is easier than base 10 arithmetic,
\n" ); document.write( "because there are less \"math facts\" that your elementary teachers would make you memorize.
\n" ); document.write( "Some are just like for base 10 arithmetic:
\n" ); document.write( "\"0%2B1=1\"
\n" ); document.write( "\"0%2B2=2\"
\n" ); document.write( "\"0%2B3=3\"
\n" ); document.write( "\"1%2B1=2\"
\n" ); document.write( "\"1%2B2=3\"
\n" ); document.write( "\"0%2A1=0\"
\n" ); document.write( "\"0%2A2=0\"
\n" ); document.write( "\"0%2A3=0\"
\n" ); document.write( "\"1%2A1=1\"
\n" ); document.write( "\"1%2A2=2\"
\n" ); document.write( "\"1%2A3=3\"
\n" ); document.write( "Some other \"math facts\" look weird, different.
\n" ); document.write( "However, you do not need to memorize them,
\n" ); document.write( "because you have already memorized more than enough.
\n" ); document.write( "Just remember that
\n" ); document.write( "when you would write a number in base 10 with a digit other that 0, 1, 2, or 3,
\n" ); document.write( "the same number would look different in base 4.
\n" ); document.write( "The number after 3 is written as 4 in base 10,
\n" ); document.write( "but you write it as 10 in base 4.
\n" ); document.write( "The number after that is written at 5 in base 10,
\n" ); document.write( "but you write it as 11 in base 4.
\n" ); document.write( "And so on, so the counting numbers in base 4 are:
\n" ); document.write( "1, 2, 3, 10, 11, 12, 13, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, ...
\n" ); document.write( "So the strange math facts are:
\n" ); document.write( "\"1%2B3=10=four\"
\n" ); document.write( "\"2%2B2=10=four\"
\n" ); document.write( "\"2%2B3=11=five\"
\n" ); document.write( "\"3%2B3=12=six\"
\n" ); document.write( "\"2%2A2=10=four\"
\n" ); document.write( "\"2%2A3=12=six\" .
\n" ); document.write( "Other than that, you use the same algorithms (procedures) for adding and multiplying.
\n" ); document.write( "You work with columns and \"carry the 1\" the same way, for example.
\n" ); document.write( "To multiply \"11321%2A12\" you start by multiplying \"11321%2A2=23302\" .
\n" ); document.write( "(It turns out that in base 4, \"11321%2A2=23302\" ) .
\n" ); document.write( "Then you multiply \"11321\" times the \"1\" from \"12\" .
\n" ); document.write( "(It is \"11321%2A1=11321\" , as it would be for base 10).
\n" ); document.write( "You write that with a \"0\" at the end,
\n" ); document.write( "as \"113210\" ,
\n" ); document.write( "right below \"23302\" ,
\n" ); document.write( "and you add them, carrying the 1's as needed.
\n" ); document.write( ". 23302
\n" ); document.write( "+113210
\n" ); document.write( "--------
\n" ); document.write( " 203112 , because\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "when you add 3+2=11 for the third digit from the right,
\n" ); document.write( "you write 1 and carry the other 1;\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "when you add \"3%2B3=12\" for the fourth digit from the right,
\n" ); document.write( "you still have to add the 1 carried over to get \"12%2B1=13\" ,
\n" ); document.write( "and you have to write 3 as the fourth digit from the right,
\n" ); document.write( "and carry the 1,\r
\n" ); document.write( "\n" ); document.write( "and for the fifth digit from the right,
\n" ); document.write( "\"2%2B1=3\" ,
\n" ); document.write( "but when you add the 1 carried over \"3=1=10\" ,
\n" ); document.write( "and you have to write the \"0\" as the fifth digit from the right,
\n" ); document.write( "and carry the 1.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It turns out that in base 4, \"11321%2A2=23302\"
\n" ); document.write( "The far right digit (the ones digit) is \"1%2A2=2\" .
\n" ); document.write( "The digit to the left of that comes from \"2%2A2=10\",
\n" ); document.write( "so that is a \"0\" , and you \"carry the 1\".
\n" ); document.write( "The digit to the left of that (the third digit from the right) comes from \"3%2A2=12=six\" ,
\n" ); document.write( "but you also have to add the \"1\" carried over,
\n" ); document.write( "so you have \"12%2B1=13\" ,
\n" ); document.write( "so you write the \"3\"} as the third digit from the right,
\n" ); document.write( "and \"carry the 1\".
\n" ); document.write( "The fourth digit from the right) comes from \"1%2A2=2\" ,
\n" ); document.write( "but you also have to add the \"1\" carried over,
\n" ); document.write( "so you have \"2%2B1=3\" ,
\n" ); document.write( "so you write the \"3\" as the fourth digit from the right.
\n" ); document.write( "The fifth digit from the right) comes from \"1%2A2=2\" ,
\n" ); document.write( "and since you have nothing carried over,
\n" ); document.write( "you just write the \"3\" as the fifth digit from the right. \n" ); document.write( "
\n" );