Solve for 2^x

Okay, I need to solve this programming question.
I have a the value 148 which equals 2^2 + 2^4 + 2^7 how can I come up with a formula that will solve for 148

Andy

 

Please clarify: are you attempting to convert an arbitrary number to binary?

At first, I thought you were going for prime factors but that's not it at
all.

 

Alright, I *think* I know what you're after. You question asks how to solve for 148, but your subject asks how to solve for x, so I'm going to assume you want an algorithm that for any number x will produce a solution that is the sum of powers of 2.

This algorithm assumes that there *is* a solution that can be derived using whole numbers.

I remember from my high-school math (amazingly!) that if a^b=c then log(c)/log(a)=b. If we look at your example of 148, we can find that log(148)/log(2)=7.2094. We can see that's "seven and a bit" so we'll take the first part of the solution as 2^7 which is 128. We subtract that from the original 148 and we're left with 20.

log(20)/log(2)=4.3219 which is "4 and a bit" so the next part of the solution is 2^4 which is 16. We subtract that from 20 and we're left with 4.

log(4)/log(2)=2 exactly so the final part of the solution is 2^2.

I hope this makes sense.

Regards

Wayne Ivory
IT Analyst Programmer
Wespine Industries Pty Ltd

 

That was exactly the answer. I’m not sure why I did not see it (maybe I was asleep in class that day )

Thanks,
Andy

 

Good one Wayne. I would have used DEC2BIN(148) and picked off the
bits. Since 2^0 = 1, I think there always is a solution.

AKS