How to convert Binary to Decimal and Octal? - binary

Question

I have a BINARY number which i want to convert it into the DECIMAL and OCTAL.
(0100 1111 1011 0010)2
I know how to convert it into the decimal. But the question making me confuse. Because middle of every 4 digits there is a space "0101 1111"
can u help me how to understand this question.
Thanks

Answer 1

First of all, make sure that number you are converting into Decimal and Octal is actually 'Binary' and not 'Binary Coded Decimal (BCD)'. Usually when the number is grouped into 4 binary digits, it represents a BCD instead of just binary.
So, once you make sure its actually binary and not BCD, the conversion to both decimal and octal are simple steps.
For binary to octal, you group the binary number into sets of 3 digits, starting form the Least Significant Bit(LSB or right-most) to the Most Significant Bit(MSB or left-most). Add leading zeros if a group of 3 digits can not be formed at the MSB.
Now convert each group of digits from binary to octal:
(000) -> 0
(001) -> 1
.
.
(111) -> 7
Finally put the numbers together, and there you have your binary converted to octal.
Eg:-
binary - 00101101
split into groups of 2: -> 000 101 101 -> 0 5 5 - > 55
Difference between'Binary Coded Decimal' and 'Binary':
For the decimal number 1248
the binary would simply be 10011100000
However, the BCD would be -> 0001 0010 0100 1000

Answer 2

The spaces are not part of the number, it's just to make it easier for humans to read. Conversion from binary to octal is simple. Group the binary digits into sets of 3 (from right to left, add extra 0s to the leftmost group, then convert each group individually. Your example:
0100 1111 1011 0010 -> 100 111 110 110 010 -> 47662

Answer 3

The space is just for readability. Especially nice if you try to convert this to hex, because 4 binary digits make up one hex-digit.

Answer 4

Firstly, those spaces are for human readability; just delete them. Secondly, If this is not for a computer program, simply open up the windows calculator, go to view, and select programmer. Then chose the bin radio button and type in your number. the qword radio button should be selected. If it's for a program, I will need to know what language to help you.

Answer 5

To convert octal to decimal very quickly there are two methods. You can actually do the actual calculation in bitshift. In programming, you should do bitshift.
Example octal number = 147
Method one: From left to right.
Step 1: First digit is one. Take that times 8 plus 4. Got 12.
Step 2: Take 12 times 8 + 7. Got 103, and 103 is the answer.
Ultimately you can use method one to convert any base into base 10.
Method one is reading from left to right of the string. Make a result holder for calculation. When you read the first leftmost digit, you add that to a result value. Each time you read a new digit, you take the result value and multiply that by the base of the number(for octal, that would be 8), then you add the value of the new digit to the result.
Method 2, bitshift:
Octal Number: 147.
Step 1: 1 = 1(bin) = Shift << 3 = 1000(result value)
Step 2: 4 = 100(bin) + 1000(result value) = 1100(result value)
Step 3: 1100(result value) Shift << 3 = 1100000
Step 4: 7 = 111(bin) + 1100000(result value) = 1100111
Step 5: 1100111 binary is 103 decimal.
In a programming loop, you can do something like the below, and it is lightning fast. The code is so simple that it can be converted into any programming language. Note that there isn't any error checking.
for ( int i = 0; i < length; i++ ){
c = (str.charAt(i) ^ 48);
if ( c > 7 ) return 0; // <- if char ^ 48 > 7 then that is not a valid octal number.
out = (out << 3) + c;
}