Question

A "bit" is a computer term for one of the digits 0 or 1. A "bit-string" of length 9 is a sequence of 9 digits, all of which are either 0 and 1.

a) How many bit strings of length 9 are there?

b) How many bit strings are between 8 and 9 bits long?

Answer 1

Part (a)

There are 2 options per bit, and 9 bits. We have 2^9 = 512 different bit strings of length 9.

Answer: 512

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Part (b)

There are 2^8 = 256 bit strings of length 8 and 2^9 = 512 bit strings of length 9.

That gives 256+512 = 768 bit strings that are between lengths 8 bits and 9 bits long.

Answer: 768