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‎docs/mining/concepts/difficulty-adjusting-algorithm.md

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# Difficulty Adjusting Algorithm
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# Difficulty Adjusting Algorithm
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How to adjust the difficulty target to ensure an average block generation time of 10 minutes.
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## What is a Difficulty Adjustment Algorithm?
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A difficulty adjustment algorithm adjusts the difficulty target based on the speed of past block production to ensure
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that new blocks are generated at an average time of 10 minutes. This algorithm is an important component of the
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blockchain network, controlling the block production speed, regulating the issuance rate of new coins, and ensuring the
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security and stability of the blockchain.
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The following explains Bitcoin's difficulty adjustment algorithm and the ASERT-DAA algorithm used in the MVC network.
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## Bitcoin's Difficulty Adjustment Algorithm
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Bitcoin adjusts its difficulty every 2016 blocks (approximately every two weeks). Here are the detailed steps of
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Bitcoin's difficulty adjustment algorithm:
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**Calculate Actual Time Taken**
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The actual time taken is the total time taken to generate the last 2016 blocks:
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$$
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\text{Actual Time} = \text{Time of the Last Block} - \text{Time of the First Block}
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$$
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**Calculate Target Time**
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The target time is the expected time to generate 2016 blocks:
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$$
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\text{Target Time} = 2016 \times 10 \, \text{minutes}
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$$
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$$
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\text{Target Time} = 2016 \times 600 \, \text{seconds}
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$$
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$$
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\text{Target Time} = 1209600 \, \text{seconds}
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$$
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**Calculate New Difficulty Target**
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The new difficulty target is adjusted based on the ratio of actual time to target time:
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$$
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\text{New Difficulty Target} = \text{Old Difficulty Target} \times \left( \frac{\text{Actual Time}}{\text{Target Time}}
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\right)
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$$
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**Limit Adjustment Range**
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To avoid drastic fluctuations in the difficulty target, the Bitcoin protocol limits the adjustment range to no more than
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four times or less than one-quarter of the previous difficulty:
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$$
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\text{New Difficulty Target} = \min\left(\text{Old Difficulty Target} \times 4, \max\left(\frac{\text{Old Difficulty
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Target}}{4}, \text{New Difficulty Target}\right)\right)
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$$
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The drawback of this method is that the adjustment speed is slow. For a mature and stable blockchain network like
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Bitcoin, this adjustment speed is acceptable. However, for emerging blockchain networks, price fluctuations may lead to
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significant changes in computing power, seriously affecting block production speed.
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When BCH (Bitcoin Cash) first forked from Bitcoin, it faced block production difficulties due to computing power
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fluctuations. BCH initially adopted the EDA (Emergency Difficulty Adjustment) algorithm to adjust the difficulty in a
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shorter time, ensuring block production speed. However, the EDA algorithm had some issues and was vulnerable to attacks.
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Therefore, BCH later adopted the ASERT-DAA algorithm, which performed well in the BCH network. Consequently, the MVC
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network also adopted the ASERT-DAA algorithm.
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## ASERT-DAA Algorithm
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The [ASERT-DAA](https://github.com/bitcoincashorg/bitcoincash.org/blob/master/spec/2020-11-15-asert.md) algorithm is a
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difficulty adjustment algorithm used in the BCH network. It is a dynamic difficulty adjustment algorithm based on
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computing power that can adjust the difficulty in a short time to ensure an average block production time of 10 minutes.
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The Automatic Difficulty Adjustment by Smoothly Updating and Real-Time Targeting (Asert) algorithm was introduced in the
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November 15, 2020, upgrade of Bitcoin Cash. Here are the features and calculation steps of the Asert difficulty
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adjustment algorithm:
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### Features of the Asert Difficulty Adjustment Algorithm
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1. **Continuous Adjustment**:
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The Asert algorithm employs a continuous difficulty adjustment mechanism instead of adjusting every 2016 blocks. This
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allows it to more promptly reflect changes in computing power and maintain a more stable block production time.
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2. **Time Parameterization**:
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Asert adjusts difficulty directly based on the difference between actual and target block production times, making
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the adjustments more flexible and precise.
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3. **Exponential Smoothing**:
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The Asert algorithm uses exponential smoothing to avoid drastic fluctuations in the difficulty target, ensuring
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smooth transitions and stability.
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### Asert Difficulty Adjustment Formula
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The core formula of the Asert algorithm is as follows:
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$$
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D_{next} = D_{prior} \times 2^{\left( \frac{t_{actual} - t_{expected}}{T} \right) / \tau}
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$$
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Where:
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- $ D_{next}$ is the difficulty target for the next block.
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- $ D_{prior}$ is the current block's difficulty target.
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- $ t_{actual}$ is the difference in timestamps between the current block and the last adjusted block.
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- $ t_{expected}$ is the target block time interval multiplied by the number of blocks.
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- $ T$ is the target block time, usually 600 seconds (10 minutes).
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- $ \tau$ is a time constant used for smoothing adjustments, typically 172800 seconds (2 days).
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### Calculation Steps
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1. **Calculate Time Difference**:
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Calculate the difference in timestamps between the current block and the last adjusted block, i.e., $ t_{actual}$.
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2. **Calculate Target Time Difference**:
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Calculate the target time difference based on the expected block time interval and the actual number of blocks,
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i.e., $ t_{expected}$.
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3. **Calculate Difficulty Adjustment Factor**:
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Use the formula to calculate the difficulty adjustment factor:
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$$
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\text{Adjustment Factor} = 2^{\left( \frac{t_{actual} - t_{expected}}{T} \right) / \tau}
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$$
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4. **Calculate Next Block's Difficulty Target**:
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Calculate the next block's difficulty target using the adjustment factor:
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$$
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D_{next} = D_{prior} \times \text{Adjustment Factor}
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$$
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### Example
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Suppose the current block's difficulty target $ D_{prior} $ is 100000, the actual time difference $ t_{actual}$ is 1200
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seconds, the target time difference $ t_{expected}$ is 600 seconds, the target block time $ T$ is 600 seconds, and the
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time constant $ \tau$ is 172800 seconds.
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1. **Calculate Time Difference**:
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$$
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t_{actual} = 1200
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$$
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$$
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t_{expected} = 600
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$$
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2. **Calculate Adjustment Factor**:
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$$
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\text{Adjustment Factor} = 2^{\left( \frac{1200 - 600}{600} \right) / 172800}
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$$
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$$
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\text{Adjustment Factor} = 2^{\left( \frac{600}{600} \right) / 172800}
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$$
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$$
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\text{Adjustment Factor} = 2^{1 / 172800}
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$$
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3. **Calculate New Difficulty Target**:
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$$
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D_{next} = 100000 \times 2^{1 / 172800}
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$$
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This calculation enables the MVC network to more smoothly adjust the difficulty, addressing computing power fluctuations
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and ensuring network stability and reliability.

‎docs/mining/concepts/difficulty-target.md

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# Difficulty Target and Network Hashrate
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An introduction to the concepts of difficulty target and network-wide difficulty.
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> Note: Difficulty target and network-wide difficulty are two different concepts. The difficulty target is the value
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> that a block's hash must be less than, while network-wide difficulty is the difficulty of obtaining the next valid
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> block. Generally, the smaller the difficulty target, the greater the difficulty; the higher the network-wide difficulty,
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> the harder it is to mine.
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## Difficulty Target
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The difficulty target is the value that a block's hash must be less than. The hash value calculated by the block header
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hash algorithm can be viewed as a 256-bit hexadecimal number. The more leading zeros in the hash value, the smaller the
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corresponding number of the hash value. The difficulty target specifies that the hash value must be less than a specific
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value, and only a hash value that meets this condition will be accepted by the network.
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The difficulty target determines the computational difficulty miners need to find a valid block hash. The difficulty
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target ensures that new blocks are discovered approximately every 10 minutes, regardless of changes in the network's
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total computational power. The entire network adjusts the difficulty target in real-time to control the speed of block
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production and the issuance rate of new coins.
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## Representation of Difficulty Target
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In the Bitcoin and MVC networks, the difficulty target is located in the `bits` field of the block header. The `bits`
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field is a 4-byte integer that represents the difficulty target value. The value of the `bits` field is a hexadecimal
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number, using a compact format to represent the difficulty target. The compact `bits` value can be calculated into the
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actual target value using the following formula:
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- **Compact Format**: In the MVC network, the difficulty target is often represented in a compact form called "bits."
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This is a 4-byte value from which the actual target hash value can be calculated.
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- **Calculating the Actual Target Value**: The actual target value can be calculated from the compact `bits` format
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using the following formula:
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$$
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\text{Target} = \text{Coefficient} \times 2^{(8 \times (\text{Exponent} - 3))}
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$$
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Where `Coefficient` is the first three bytes of `bits`, and `Exponent` is the last byte of `bits`. For example,
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if `bits` is represented as `0x1d00ffff`, then `Coefficient` is `0x00ffff` and `Exponent` is `0x1d`.
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![img.png](/img/blockheader-bits.png)
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### Example
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Suppose the current difficulty target is represented as `0x1b0404cb`. We can calculate the actual difficulty target
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value with the following steps:
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**Extracting the Coefficient and Exponent**:
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$$
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\text{Coefficient} = 0x0404cb
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$$
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$$
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\text{Exponent} = 0x1b
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$$
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**Calculating the Actual Target Value**:
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$$
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\text{Target} = 0x0404cb \times 2^{(8 \times (0x1b - 3))}
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$$
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$$
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\text{Target} = 0x0404cb \times 2^{(8 \times 0x18)}
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$$
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$$
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\text{Target} = 0x0404cb \times 2^{192}
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$$
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In hexadecimal form:
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$$
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\text{Target} = 0x0023AEA3C73B13B193EC4E9D9AD4A03B60000000000000000000000000000000
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$$
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This value is the actual difficulty target value. The block header's hash value must be less than this value to be
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accepted by the network. In other words, if the calculated hash value of the block header is less than this value (
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starting with 2 leading zeros), then the block is valid.
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## Difficulty Calculation
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Network-wide difficulty is the difficulty of obtaining the next valid block. It is determined by the total computational
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power of all miners in the network. Network-wide difficulty is a dynamic value that adjusts in real-time based on the
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total computational power of miners. The goal of network-wide difficulty is to ensure that new blocks are discovered
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approximately every 10 minutes.
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You can use the mvc-cli command-line tool to check the current network-wide difficulty:
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```bash
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mvc-cli getmininginfo
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```
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```text
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{
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"blocks": 71434,
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"currentblocksize": 339,
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"currentblocktx": 1,
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"difficulty": 34975994469.53414,
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"errors": "",
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"networkhashps": 2.409330669323676e+17,
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"pooledtx": 1,
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"chain": "main"
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}
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```
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In the output above, the `difficulty` field represents the current network-wide difficulty in decimal format. The higher
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the difficulty value, the harder it is to mine.
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Network-wide difficulty can be calculated inversely from the difficulty target. The smaller the difficulty target, the
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higher the difficulty, so it is essential to define what difficulty is.
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### Maximum Target (Also Known as Difficulty 1)
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In the MVC network, the difficulty value is a relative measure used to indicate the difficulty of finding a valid block
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hash. It is calculated by comparing the current target with the maximum target (Max Target). The maximum target is the
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target value at the lowest difficulty, which is the initial difficulty target of MVC.
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The maximum difficulty target (Max Target) is:
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$$
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\text{Max Target} = 0x1d00ffff
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$$
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In decimal format, the maximum target is:
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$$
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\text{Max Target} = 0x1d00ffff \times 2^{8 \times (0x1d - 3)}
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$$
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$$
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\text{Max Target} = 0x00ffff \times 2^{8 \times 0x1a}
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$$
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$$
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\text{Max Target} = 65535 \times 2^{208}
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$$
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### Calculating Difficulty Value
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The difficulty value is calculated by dividing the maximum target by the current target:
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$$
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\text{Difficulty} = \frac{\text{Max Target}}{\text{Current Target}}
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$$
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This aligns with our understanding that the smaller the current target, the higher the difficulty value. As it is a
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ratio, the difficulty value of the maximum difficulty target is the smallest, which is 1.
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### Steps to Calculate Difficulty Value
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**Convert Current Difficulty Target to Decimal**:
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$$
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\text{Current Target} = 165608837515678774353553029698295978246167310057892115125170688
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$$
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**Calculate the Decimal Value of the Maximum Target**:
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$$
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\text{Max Target} = 65535 \times 2^{208}
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$$
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$$
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\text{Max Target} \approx 5.788 \times 10^{49}
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$$
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**Divide to Calculate the Difficulty Value**:
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$$
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\text{Difficulty} = \frac{5.788 \times 10^{49}}{165608837515678774353553029698295978246167310057892115125170688}
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$$
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Approximately, the difficulty value is:
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$$
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\text{Difficulty} \approx \frac{5.788 \times 10^{49}}{1.656 \times 10^{41}}
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$$
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$$
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\text{Difficulty} \approx 3.493 \times 10^8
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$$

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