blockchain – How does fixing a block work in relation to the primary letter/quantity after the 0’s?

The comparability used is numeric

These are numbers not strings of characters. You possibly can see this by wanting on the code within the 2009 important.cpp of the Bitcoin reference implementation:

        uint256 hashTarget = CBigNum().SetCompact(pblock->nBits).getuint256();
        uint256 hash;

[...]

           if (hash <= hashTarget)
            {
                pblock->nNonce = tmp.block.nNonce;
                assert(hash == pblock->GetHash());

                    //// debug print
                    printf("BitcoinMiner:n");
                    printf("proof-of-work discovered  n  hash: %s  ntarget: %sn", hash.GetHex().c_str(), hashTarget.GetHex().c_str());

Be aware that if (hash <= hashTarget) is a numeric comparability. Each hash and hashTarget are kind uint256 – an unsigned integer.

Numbers expressed in hexadecimal are nonetheless numbers

There’s a selection of visible representations however the selection made doesn’t change the underlying nature of the quantity or the best way wherein numbers are in contrast arithmetically or at a machine degree in a pc.

Your instance, 00005fad, is a quantity expressed in hexadecimal (base 16), the identical quantity will be written in regular decimal (base 10) as 24493. Anybody unfamiliar with non-decimal representations corresponding to hexadecimal, octal and binary can test this utilizing one thing just like the Home windows 10 calculator, within the menu select “Programmer Mode” then click on on “hex” and enter 5fad – it exhibits the similar worth in a number of completely different representations.

Possibly this may make it clearer?

Though the block hashes have the identical variety of main zeroes, one is a failure and the opposite a hit.

Main zeroes

The notion that Bitcoin cares concerning the variety of main zeroes in, say, a hexadecimal illustration, is a generally repeated mistake (do not ask me how I do know this).

When you insist on writing numbers with main zeroes it’s nonetheless clearly true that 000015 (fifteen) with 4 main zeroes is smaller than 000150 (100 and fifty) with solely three main zeroes. It could nonetheless be a mistake to suppose that smaller numbers at all times have extra main zeroes. Each you and Bitcoin know that 000017 (seventeen) is smaller than 000019 (nineteen) though each have the identical variety of main zeroes.

It’s true that a is lower than b in precisely the identical manner that 7 is lower than 8 or that 2 is lower than 3. However it’s most likely a mistake to begin evaluating particular person digits in a selected visible illustration. The hash and hash targets are atypical numbers (although massive) which can be in contrast in an atypical manner.

So the place does this speak of main zeroes come from? Based on a distinguished contributor:

hashcash, the unique PoW system, had a “problem” that was really the variety of zero bits up entrance within the hash. Bitcoin’s proof of labor is predicated on it, however generalized to an enormous integer comparability.

See

Examples

Lets take a look at some current blocks (most up-to-date at high, reverse chronological order)

Discover that the problem elevated after block 669311 however the variety of main zeroes within the hashes has not elevated (not in hexadecimal and never in binary).

Implementations

If you wish to see precise particulars you would take a look at early variations of the Bitcoin reference implementation in C++. Nevertheless I’d counsel as a substitute wanting on the present BTCD implementation in go-lang as a result of that’s properly commented and, in my view, a neater language to learn.

e.g. https://github.com/btcsuite/btcd/blob/grasp/chaincfg/params.go

    // TargetTimespan is the specified period of time that ought to elapse
    // earlier than the block problem requirement is examined to find out how
    // it must be modified to be able to preserve the specified block
    // technology charge.
    TargetTimespan time.Period

    // TargetTimePerBlock is the specified period of time to generate every
    // block.
    TargetTimePerBlock time.Period

and https://github.com/btcsuite/btcd/blob/grasp/blockchain/problem.go

    // Calculate new goal problem as:
    //  currentDifficulty * (adjustedTimespan / targetTimespan)
    // The outcome makes use of integer division which implies it will likely be barely
    // rounded down.  Bitcoind additionally makes use of integer division to calculate this
    // outcome.
    oldTarget := CompactToBig(lastNode.bits)
    newTarget := new(large.Int).Mul(oldTarget, large.NewInt(adjustedTimespan))
    targetTimeSpan := int64(b.chainParams.TargetTimespan / time.Second)
    newTarget.Div(newTarget, large.NewInt(targetTimeSpan))

Calculating the hash goal

See