Mysitque
2013-09-29 10:12:09 UTC
Base Conversion
One algorithm for converting a base 10 number to another base b involves repeatedly dividing by b. Each time a division is
performed the remainder and quotient are saved. At each step, the dividend is the quotient from the preceding step; the
divisor is always b. The algorithm stops when the quotient is 0. The number in the new base is the sequence of remainders in
reverse order (the last one computed goes first; the first one goes last).
In this exercise you will use this algorithm to write a program that converts a base 10 number to a 4-digit number in another
base (you don't know enough programming yet to be able to convert any size number). The base 10 number and the new base
(between 2 and 9) will be input to the program. The start of the program is in the file BaseConvert.java. Save this file to your
directory, then modify it one step at a time as follows:
1. The program will only work correctly for base 10 numbers that fit in 4 digits in the new base. We know that in base 2 the
maximum unsigned integer that will fit in 4 bits is 11112 which equals 15 in base 10 (or 24 – 1). In base 8, the maximum
number is 77778 which equals 4095 in base 10 (or 84 – 1). In general, the maximum base 10 number that fits in 4 base b
digits is b4 – 1. Add an assignment statement to the program to compute this value for the base that is input and assign it
to the variable maxNumber. Add a statement that prints out the result (appropriately labeled). Compile and run the
program to make sure it is correct so far.
2. Now add the code to do the conversion. The comments below guide you through the calculations—replace them with the
appropriate Java statements.
// First compute place0 -- the units place. Remember this comes
// from the first division so it is the remainder when the
// base 10 number is divided by the base (HINT %).
// Then compute the quotient (integer division / will do it!) -
// You can either store the result back in base10Num or declare a
// new variable for the quotient
// Now compute place1 -- this is the remainder when the quotient
// from the preceding step is divided by the base.
// Then compute the new quotient
// Repeat the idea from above to compute place2 and the next quotient
// Repeat again to compute place3
3. So far the program does not print out the answer. Recall that the answer is the sequence of remainders written in reverse
order— note that this requires concatenating the four digits that have been computed. Since they are each integers, if we
just add them the computer will perform arithmetic instead of concatenation. So, we will use a variable of type String.
Note near the top of the program a variable named baseBNum has been declared as an object of type String and
initialized to an empty string. Add statements to the program to concatenate the digits in the new base to baseBNum and
then print the answer. Compile and run your program. Test it using the following values: Enter 2 for the base and 13 for
the base 10 number—the program should print 1101 as the base 2 value; enter 8 for the base and 1878 for the number—
the program should print 3526 for the base 8 value; enter 3for the base and 50 for the number—the program should print
1212.
If someone could help me get started, that would be great. I need the help ASAP. Thanks. :)