Why is the maximum target truncated?

Why is the maximum target truncated?

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?

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