algorithm - Intuition for this statement: given a random hashed set, a sequence of k zero bits in the beginning indicate there is approximately 2^k elements -


i trying understand hyperloglog, , while doing have encountered statement need further explanation , intuition on.

in 1 blog explaining hyperloglog, claim following

given random hashed set, sequence of k 0 bits in element occur once in every 2^k elements, 2^k approximation of how large cardinality

which assume implies

00000001

will occur 1 time every 2^7 elements.

but statement confusing me, since isn't combination of 0 , 1 pattern k bit occur 1 time every 2^k element?

what make consecutive 0s special?


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