user63709: Reading the docs on target:

The maximum target used by SHA256 mining devices is:
0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
Because Bitcoin stores the target as a floating-point type, this is truncated:
0x00000000FFFF0000000000000000000000000000000000000000000000000000

I know that the purpose is to force miners to generate hashes with a value lower than the target. But the docs are vague, why is this truncation required? And then, why truncate after the first four Fs?

user10411: Target is stored in block header (it's called Bits), and it takes only 4 bytes. We derive target 256-bit value from these 32 bits. That's why it is getting truncated.
There is no need to store all 256 bits, or even 224 bits (if we assume first 4 bytes are zero). We don't need such precision.
You can read in wiki, how target is getting calculated from Bits.
You can also check my answer here, with example: 
How does difficulty is defined for block '55798'?

63709: <p>Reading the docs on <a href="https://en.bitcoin.it/wiki/Target" rel="nofollow noreferrer">target</a>:</p>

<blockquote>
  <p>The maximum target used by SHA256 mining devices is:</p>
  
  <p>0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF</p>
  
  <p>Because Bitcoin stores the target as a <strong>floating-point type</strong>, this is truncated:</p>
  
  <p>0x00000000FFFF0000000000000000000000000000000000000000000000000000</p>
</blockquote>

<p>I know that the purpose is to force miners to generate hashes with a value lower than the target. But the docs are vague, why is this truncation required? And then, why truncate after the first four Fs?</p>
 10411: <p>Target is stored in block header (it's called Bits), and it takes only 4 bytes. We derive target 256-bit value from these 32 bits. That's why it is getting truncated.</p>

<p>There is no need to store all 256 bits, or even 224 bits (if we assume first 4 bytes are zero). We don't need such precision.</p>

<p>You can <a href="https://en.bitcoin.it/wiki/Difficulty#How_is_difficulty_stored_in_blocks.3F" rel="nofollow noreferrer">read in wiki</a>, how target is getting calculated from Bits.</p>

<p>You can also check my answer here, with example: 
<a href="https://bitcoin.stackexchange.com/questions/75625/how-does-difficulty-is-defined-for-block-55798/75627#75627">How does difficulty is defined for block &#39;55798&#39;?</a></p>
