hashing by division

Hashing using division method means h(k) = k mod m . I read that

m should not be power of 2. This is because if m = 2^p, h becomes just the p lowest-order bits of k. Usually we choose m to be a prime number not too close to a power of 2.

Could someone explain with a small example the lowest order bits part? I thought all (mod m) does is that it wraps the result around a range m. Somehow cant see the issue if m was power of 2.

Let k be 27 (= 00011011), and m be 16 (= 00010000) which is 2^4

then k%m = 11 (= 1011) which are same as last 4 bits of k.

You should try other examples as well on your own to convince yourself.

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