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1845 in base 10.
\n" ); document.write( "in base 13 it would be:
\n" ); document.write( "i believe the answer will be ABC
\n" ); document.write( "that would be:
\n" ); document.write( "C * 13^0 = 12 * 1 = 12 plus:
\n" ); document.write( "B * 13^1 = 11 * 13 = 143 plus:
\n" ); document.write( "A * 13^2 = 10 * 169 = 1690 equals:
\n" ); document.write( "1845
\n" ); document.write( "-----
\n" ); document.write( "the logic used is to divide the number in the base 10 by the base that you are wanting to convert to.
\n" ); document.write( "you would divide 1845 by 13 to get a quotient of 141 and a remainder of 12.
\n" ); document.write( "you would then divide 141 by 13 to get a quotient of 10 and a remainder of 11.
\n" ); document.write( "you would then divide 10 by 13 to get a quotient of 0 and a remainder of 10.
\n" ); document.write( "-----
\n" ); document.write( "your answer is in the order of the remainders from bottom to top.
\n" ); document.write( "your order is 10, 11, 12.
\n" ); document.write( "in the base of 13, 10 would be equal to A and 11 would be equal to B and 12 would be equal to C.
\n" ); document.write( "that makes your number in the base of 13 equal to ABC.
\n" ); document.write( "-----
\n" ); document.write( "the base 10 value of any base system is equal to the base 10 value of the least significant digit times the base raised to the 0 power plus the base 10 value of the next significant digit times the base raised to the 1 power plus the base 10 value of the next significant digit times the base raised to the 2 power, etc., until there are no more significant digits to process.
\n" ); document.write( "-----
\n" ); document.write( "the base 10 value of the number 1845 in the base of 10 is therefore equal to:
\n" ); document.write( "5 * 10^0 + 4 * 10^1 + 8 * 10^2 + 1 * 10^3 which becomes:
\n" ); document.write( "5 * 1 + 4 * 10 + 8 * 100 + 1 * 1000 which becomes:
\n" ); document.write( "5 + 40 + 800 + 1000 which becomes:
\n" ); document.write( "1845
\n" ); document.write( "-----
\n" ); document.write( "the base 10 value of the number ABC in the base of 13 is therefore equal to:
\n" ); document.write( "C * 13^0 + B * 13^1 + A * 13^2 which becomes:
\n" ); document.write( "C * 1 + B * 13 + A * 169 which becomes:
\n" ); document.write( "12 * 1 + 11 * 13 + 10 * 169 which becomes:
\n" ); document.write( "12 + 143 + 1690 which becomes:
\n" ); document.write( "1845
\n" ); document.write( "-----
\n" ); document.write( "in any base where the value of the digits in each position is greater than 9, alphabetic characters are used to represent the higher number.
\n" ); document.write( "-----
\n" ); document.write( "in the base 16 (hexadecimal system), therefore:
\n" ); document.write( "10 = A
\n" ); document.write( "11 = B
\n" ); document.write( "12 = C
\n" ); document.write( "13 = D
\n" ); document.write( "14 = E
\n" ); document.write( "15 = F
\n" ); document.write( "each position goes up to 15.
\n" ); document.write( "the number 17 in the hexadecimal system would be equal to:
\n" ); document.write( "17 divided by 16 equals a quotient of 1 with a remainder of 1.
\n" ); document.write( "quotient of 1 divided by 16 equals a quotient of 0 with a remainder of 1.
\n" ); document.write( "the hexadecimal equivalent number would be equal to 11.
\n" ); document.write( "the base 10 equivalent of tht number would be:
\n" ); document.write( "1 * 16^0 + 1 * 16^1 which would be equal to:
\n" ); document.write( "1 + 16 which would be equal to:
\n" ); document.write( "17.\r
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