# Base conversion

posted 10 years ago

I have the SCJP exam in 2 weeks and would like to know a simple way to remember number base conversions.

i.e:

System.out.println(0107);

How would one, before viewing the result, calculate this the simplest way posible?

i.e:

System.out.println(0107);

How would one, before viewing the result, calculate this the simplest way posible?

SCJP 1.4, SCWCD 1.4, SCBCD 1.3, SCJD, SCEA/OCMJEA

Live life to an interface, not an implementation!

Sergei Iakhnin

Ranch Hand

Posts: 53

posted 10 years ago

To convert any base number with n digits to decimal do the following:

1) Number the digits right to left from 0 to n-1.

In your case, 0107 is actually 107 and the leading 0 tells us its in octal.

so we have

107 <--- number

210 <--- digit numbers

2) now calculate the following sum. For each digit, multiply the digit by the number base to the power of the digit number, and add to the total.

In the case of 107 octal we have

1*8^2 + 0*8^1 + 7*8^0 = 64 + 0 + 7 = 71 (decimal)

To convert from binary to octal take the binary number and group the digits in threes starting from right to left. Convert each three binary digits to an octal digit and you have the number.

To convert from binary to hex take the binary number and group the digits in fours starting from right to left. Convert each four binary digits to a hex digit and you have the number.

So if you have the number 11110010100101

To octal we have

11 110 010 100 101

3 6 2 4 5

so we get 36245 octal

To hex we have

11 1100 1010 0101

3 c a 5

so we get 3ca5

1) Number the digits right to left from 0 to n-1.

In your case, 0107 is actually 107 and the leading 0 tells us its in octal.

so we have

107 <--- number

210 <--- digit numbers

2) now calculate the following sum. For each digit, multiply the digit by the number base to the power of the digit number, and add to the total.

In the case of 107 octal we have

1*8^2 + 0*8^1 + 7*8^0 = 64 + 0 + 7 = 71 (decimal)

To convert from binary to octal take the binary number and group the digits in threes starting from right to left. Convert each three binary digits to an octal digit and you have the number.

To convert from binary to hex take the binary number and group the digits in fours starting from right to left. Convert each four binary digits to a hex digit and you have the number.

So if you have the number 11110010100101

To octal we have

11 110 010 100 101

3 6 2 4 5

so we get 36245 octal

To hex we have

11 1100 1010 0101

3 c a 5

so we get 3ca5

SCJP 1.4, SCWCD 1.4