Truncating A Hash

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What is the down side of truncating a hash?  For example, an SHA-256 
hash is 256 bits.  Is it any less secure if one was to drop the last 128 
bits to make a 128 bit hash or take the MD5 hash of the SHA-256 hash to 
get a 128 bit hash?  It does not seem that such an action would make it 
any easier to brute force reverse the hash, but then again, I am clearly 
not a security expert.

Jay


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