ISRO | ISRO CS 2014 | Question 19

The number of bit strings of length 8 that will either start with 1 or end with 00 is?
(A) 32
(B) 128
(C) 160
(D) 192


Answer: (C)

Explanation:
(I) Number of 8 bit strings starting with 1 : 1 _ _ _ _ _ _ _ = 2⁷ = 128
(II) Number of 8 bit strings ending with 00 : _ _ _ _ _ _ 00
It has 2 possibilities:
if the string starts with 0 then total strings = 2⁵ = 32
and if the string starts with 1 then total strings = 32 but they are already covered in all the strings starting with 1
So, total number of strings = 128 + 32 = 160


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