How to convert an exponent to binary number?

[MathematicalPhysicist]

how to convert an exponent to binary number?

 

[chroot]

What you say does not make much sense -- you can convert any number into any base you want.

Please provide an example of what you're trying to do so that we can help you better.

- Warren

 

[MathematicalPhysicist]

i read the next statement at this webpage:http://www.mersenne.org/math.htm
"Convert the exponent 23 to binary, you get 10111."

 

[Lonewolf]

That's not an exponent, just a number in binary form. To convert we do the following

16 8 4 2 1
1 0 1 1 1

So, we have one 16, no 8, one 4, one 2, and one 1. We sum them to get 16+4+2+1=23. The division algorithm can be used to convert from decimal to binary.

23-16=7, so we put a 1 in the 16 column.
7-8<0, so we put a 0 in the 8 column.
7-4=3. so we put a 1 in the 4 column.
3-2=1, so we put a 1 in the 2 column.
2-1=1, so we put a 1 in the 1 column.

Thus, 23 in binary form is 10111.

 

[HallsofIvy]

The thing that was confusing was that you were asking about
"converting an exponent". You are really just asking about converting a number. The fact that the number happens to be an exponent in the formula is not important.

Another way to do the same thing is:

2 divides into 23 11 times with remainder 1
2 divides into 11 5 times with remainder 1
2 divides into 5 2 times with remainder 1
2 divides into 2 1 time with remainder 0
2 divides into 1 0 times with remainder 1

Now that we have reached "0 times" write the remainders in reverse order : 10111 base 2 is 23 base 10.

 

[Integral]

HallsofIvys methods works for conversion from base 10 to any base, simply divide by the base, the remainder gives the digits in the new base, starting with the least significant.