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Couldn't you use brute force to guess someone’s binary number because it's 1 or 0 - 256 times then just keep switching 1's and 0's around- which then can be converted hexadecimal to guess their bitcoin private key?

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Yes, in theory, you could just brute-force every secret there is. In practice, it's not feasible.

A practical demonstration

I'm going to think of a random number between 0 and 10, and you will have to guess which one it is. Did you make your guess? Correct, it was 2! Even if you did not make your guess correctly, if I would stay with the same number and you could keep guessing, sooner or later you would have exhausted all options and found the number.

Now I will think of a random number between 0 and 115792089237316195423570985008687907853269984665640564039457584007913129639935, and again you have to guess. Did you make your guess?

I'm fairly confident that you guessed wrong. In fact, I could keep you guessing for a full year, and you wouldn't be able to find it. You could even rent a server farm in the Arctic, let that server farm make billions and billions of guesses per second, and I am still confident you wouldn't guess my number, just because of how absurdly large it is.

If you would like to know more about a physical demonstration that it's impossible, even if we were to invent faster and faster CPU's, look at this beautiful answer by Thomas Pornin.