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When you are looking at a binary number, the number of zeros at the start is the exact same thing as making sure the number is below a certain threshold.


Not exactly the same thing. Consider this example:

Threshold is 001010

The numbers 001001 and 001011 have the same number of leading zeroes but one is below the threshold and the other is not.


What I said is correct, but I suppose ambiguous. What I mean to say is that counting MSB zeros does specify that the number will be below a threshold, just not an arbitrary threshold like the one you gave in your example.

For a more concrete example, if the requirement is that a 16-bit word is less than 4096, you only have to verify that it leads with 4 zeros.


Yes but Bitcoin uses 'below number X' which has more precision than just counting leading zeroes.


No it's not the exact same thing.

Example:

Treshold = 001010

If you check 001011 or 001001 then the number of leading zeros are the same but one number is below the threshold and the other is not.




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