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How do you derive "0x008000 is the smallest legal value for the lower 24 bits since targets are always stored with the lowest possible exponent"?

Bitcoin Stack Exchange

Bitcoin News / Bitcoin Stack Exchange 182 Views

If we used any number less than 0x008000 in the lower 24 bits, then the exponent could be lowered, violating the rule that "targets are always stored with the lowest possible exponent."

For example, 0x05007fff (big endian) has exponent 0x05, so this represents 0x007fff * 2^(16). Then we could have written 0x047fff00 to represent the same number, because

0x7fff00 * 2^8 = 0x007fff * 2^16

You cannot do the same with 0x008000 though, because attempting to reduce the exponent and multiply the mantissa by 2^8 will produce a mantissa of 0x800000, which is negative (the 24th bit is a sign bit). the difficulty target must be a positive number, so this sign bit must always be set to 0.


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