What is 1000000100100110 in decimal, hexadecimal, and base 36?

Question

kropot72 · Answer

The value in decimal is found from the following:
$$2^{1}+2^{2}+2^{5}+2^{8}+2^{15}=$$
Can you calculate the answer?

kropot72 · Answer

@aetteews Are you there?

anonymous · Answer

Yup, sorry, was taking awhile for people to respond... 2+2^2+2^3+2^5+2^8+2^15 = 33062

kropot72 · Answer

You are correct

anonymous · Answer

Okay, so that gets me to decimal...

anonymous · Answer

So how do I convert to hexadecimal?

anonymous · Answer

Okay... so 16^3 = 4096 and 16^4 = 65536... so 16^3 is less than 33062. So then 33062 - 16^3 = 28966.

anonymous · Answer

Okay, I think I remember this, do you use the modulus (%) operator for this part?

kropot72 · Answer

First find the highest power of 16 that will divide into 33062. Then find the highest number that can be multiplied with 4096 to be less than 33062 (ignore the second step I gave before)

anonymous · Answer

Divide into? You mean evenly?

anonymous · Answer

So 33062/16^3= 8.07177734

kropot72 · Answer

No. Not evenly. In this case there will be a remainder that will be treated next.

anonymous · Answer

Okay, so the remainder can be calculuted using modulus. So the remainder is 294.

kropot72 · Answer

So 8 is the most significant digit of the hexadecimal answer. 16^2 will divide into 294 with remainder 38. So 1 is the next digit of our solution.

anonymous · Answer

Oh, okay, so then you do the same thing again?
294/16^2=1.1484375
294%16^2= 38
38/16=2.37500
38%16=6
What now?

kropot72 · Answer

The full hex number is 8126. Can you see how it was obtained.

anonymous · Answer

Yup, it's the 8 from the first part 33062/16^3= 8.07177734 the 1 is from 294/16^2=1.1484375 and the 2 is from 38/16=2.37500, so I guess the remainder once you can't divide out anymore becomes your last digit?

kropot72 · Answer

You are right. The least significant digit is one of the 16 hex numbers 0,1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. The least significant digit is simply the number of units (16^0 = 1).
Sorry I need to go now. Perhaps someone else can help you now.

anonymous · Answer

I think I've got it, thanks for the help! :)

kropot72 · Answer

Great. I enjoyed working with you :)