The first laboratory exercise requires you to code two conversion schema’s in Java. Question 1 – Base number conversion

The first laboratory exercise requires you to code two conversion schema’s in Java.
Question 1 – Base number conversion.
The first programming exercise requires you to code the general algorithm to convert any
numeric base system number to base 10 (decimal). This implies any base system from base
2 (binary) to base 9. The following algorithm gives the description of the procedure.
Algorithm 1 Base b conversion to decimal
Input: A number dn−1dn−2 . . . d1d0 in base b
Output: Equivalent decimal number
1: procedure The digits of the input number are processed from left to
right one digit at a time.
2: Result = 0
3: for (i = n −1 downto 0) do
4: Result = (Result x b) + di
5: end for
6: return Result
7: end procedure
Using Algorithm 1 as the template, code the conversion routine. You are not allowed to use
any inbuilt language specific conversion commands. Your code should be able to convert any
base from 2 till 9 to decimal.
The algorithm should do the following:
1. Ask the user to enter the required base.
2. Check if the base is between 2 and 9 inclusive.
3. If not, ask the user again to enter the base.
4. Using the given equation, compute the decimal equivalent number in a for loop starting
from the left to the right.
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5. Display the decimal number in console.
The output should be formatted exactly in the shown invocation samples.
Please enter a base from 2 – 9: 2
Enter a base 2 number: 100101
The equivalent number in base 10 format is 37
Please enter a base from 2 – 9: 16
Incorrect base system. Please enter a base from 2 – 9:
Please enter a base from 2 – 9: 8
Enter a base 8 number: 247
The equivalent number in base 10 format is 167
The submission is a program named BaseToDecimal. All codes should have appropriate
documentation.
Question 2 – Decimal to binary, octal and hexadecimal number conversion.
The second programming exercise requires you to code the general algorithm to convert a
base 10 (decimal) number to a base 2 (binary), base 8 (octal) and base 16 (hexadecimal)
number. The following Algorithm 2 gives the description of the procedure.
Algorithm 2 Decimal to base b conversion
Input: A number dn−1dn−2 . . . d1d0 in decimal
Output: Equivalent number in the target base b number system
1: procedure Result digits are obtained from left to right. In the follow-
ing, MOD represents the modulo operator and DIV the integer divide
operator.
2: Quotient = decimal number to be converted
3: while (Quotient ∕= 0) do
4: Remainders (next most significant digit of result) = Quotient MOD b
5: Quotient = Quotient DIV b
6: end while
7: return Remainders
8: end procedure
An example for converting the decimal number 167 into its equivalent binary, octal and
hexadecimal numbers is shown in Tables 1 – 3.
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Table 1: Decimal to binary conversion
Quotient Remainder
167/2 = 83 1
83/2 = 41 1
41/2 = 20 1
20/2 = 10 0
10/2 = 5 0
5/2 = 2 1
2/2 = 1 0
1/2 = 0 1
Table 2: Decimal to octal conversion
Quotient Remainder
167/8 = 20 7
20/8 = 2 4
2/8 = 0 2
Table 3: Decimal to hexadecimal conversion
Quotient Remainder
167/16 = 10 7
10/16 = 0 A
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The desired base numbers can be obtained by writing the remainders generated in the reverse
order from left to right. For this example, the binary number is 10100111B , octal number is
247O and hexadecimal number is A7H .
Using Algorithm 2 as the template, code the conversion routine. You are not allowed to use
any inbuilt language specific conversion routines for bases.
The output should be formatted exactly as in the shown invocation sample below.
Please enter a base 10 number: 167
Base 2: 1 0 1 0 0 1 1 1
Base 8: 2 4 7
Base 16: A 7
The submission is a program named DecimalToBase. All codes should have appropriate
documentation