Solution: 2019 Winter Midterm - 1

Author: Michiel Smid

Question

Consider bitstrings of length 13. The positions in these strings are numbered as $1,2,3,\dots,13$. How many such bitstrings have the property that all bits at the odd positions are equal?

(a)

256

(b)

(c)

(d)

128

Solution

There are 2 choices for the odd positions: 0 or 1.

There are 6 even positions that can each be 0 or 1, so there are $ 2^6 $ ways to choose the characters for the even positions.

Thus, there are $ 2 \cdot 2^6 =2 \cdot 64 = 128 $ such bitstrings.