binary to duodecimal

[CompSci]

can some help me, i need to learn how to convert binary(base 2) to duodecimal (base 12)

 

i.e this is the binary i need to convert 01010010

 

here is the binary in other bases if u need them

 

base 8 = 122

base 10 = 82

base 16 = 52

 

plz can you include a step by step solution

 

thanks

[conzer16]

I dont know how to do it, but here is a website that will

 

http://www.convertworld.com/en/numerals/Binary.html

[CompSci]

I dont know how to do it, but here is a website that will

 

http://www.convertworld.com/en/numerals/Binary.html

 

great nice one ( i can check my answers ), but i need to know how to do it manually :horse: , for my exam

[conzer16]

Try reading this tutorial, it's a little confusing, but you should get the jist of it

[BGS]

Okay. The way I'd convert smallish binary numbers into hexadecimal or base 12 or whatever is to first convert it into base 10 (our numbers) (I'm guessing you know how to do this but if you don't then just reply and ask)

 

So 01010010 in base ten, or our normal numbering system is 82.

 

Now if you're wanting to convert to duodecimal (base 12) then divide this number by 12.

 

82 / 12 = 6 r10

 

So 12 goes into 82 6 times exactly. So the first digit would be a 6.

 

Now, for the second digit.

 

Because we have no single digit numbers for anything higher than 9, when using bases higher than 10, anything higher than 9 is represented by a letter.

 

You have a remainder of 10 and as this is one above 9 it is represented by the letter A.

 

So your binary number converted into duodecimal is 6A

[fatnickc]

So 01010010 in base ten, or our normal numbering system is 82.

 

Now if you're wanting to convert to duodecimal (base 12) then divide this number by 12.

 

82 / 12 = 6 r10

 

So 12 goes into 82 6 times exactly. So the first digit would be a 6.

 

Now, for the second digit.

 

Because we have no single digit numbers for anything higher than 9, when using bases higher than 10, anything higher than 9 is represented by a letter.

 

You have a remainder of 10 and as this is one above 9 it is represented by the letter A.

 

So your binary number converted into duodecimal is 6A

 

Indeed. You can just think of finding that number as counting up from zero the decimal number of times with the digit set of the format you want it. For example, the digit set of duodecimal is 0,1,2,3,4,5,6,7,8,9,A,B , soto count to decimal 17 you would need to go through 17 numbers other than 0, ie 0,1,2,3,4,5,6,7,8,9,A,B,10,11,12,13,14,15.

BGS's method is actually the same thing, but it is much quicker to do because it uses the fact that dividing will leave you with the number in the largest 'column' used.

[CompSci]

Okay. The way I'd convert smallish binary numbers into hexadecimal or base 12 or whatever is to first convert it into base 10 (our numbers) (I'm guessing you know how to this but if you don't then just reply and ask)

 

So 01010010 in base ten, or our normal numbering system is 82.

 

Now if you're wanting to convert to duodecimal (base 12) then divide this number by 12.

 

82 / 12 = 6 r10

 

So 12 goes into 82 6 times exactly. So the first digit would be a 6.

 

Now, for the second digit.

 

Because we have no single digit numbers for anything higher than 9, when using bases higher than 10, anything higher than 9 is represented by a letter.

 

You have a remainder of 10 and as this is one above 9 it is represented by the letter A.

 

So your binary number converted into duodecimal is 6A

 

i knew you had to divide by the base number if you want to convert anything back from base 10, but i didn't understand the remainder part i.e

 

82/12 = 6.83333333333333

 

how did you get a remainder of 10? (this the only part the that confuses me in book and tutorials)

 

plz help

[BGS]

I'm sure a lot of calculators have a function which will give you a remainder instead of the answer as a decimal but it depends what calculator you're using there.

 

In an exam it's probably easiest to just work it out yourself. I find the easiest way to divide is to do it as a multiplication sum, multiplying the base number until I get near the number I want to convert.

 

ie..

 

If I want to find out what 82/12 is then my mind process goes

 

12 * 5 = 60 Hmmm, another 12 can fit in there

12 * 6 = 72 Since another 12 on top of that would be 84 then the answer must be 6 remainder something.

 

82 - 72 = 10. The answer is 6 remainder 10

 

Basically, it's just knowing your times tables. If you find it tough sometimes then do like I did and go for the easiest numbers to multiply first, like 5 or 10 and just add and subtract after that.

[Bogbas]

Basically using this method you can get the remainder just by using your head and a piece of paper(calculator speeds up the process though). First you see how many times (whole)12 goes to 82 which is 6. Then you multiply the answer 6 with 12, which gives you 72. You then proceed to subtract the 72 from 82 leaving you with 10. Which is the remainder of the divide. Probably there's a better way to explain this, but this is how I'd do it.

 

The method I used can also be continued so you'd get the 6.83333.... but as you only want to get the remainder there's no point in going further.

[Ginger_Chris]

Another way of getting the remainder:

 

82/12 = 6.83333333333333

 

6.8333333333 - 6 = 0.83333333333

 

0.83333333333*12=10=A

 

Just multiply whatever the decimal point part isby what you originally divided by. The way is probably as fast as Bogbas's way, but probably faster when the original decimal number is greater that 144, as you have to find the remainder twice, and with larger numbers.

[CompSci]

wow awesome guys thanks for all your inputs, i finally understand

 

nice one guys thanks again