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. 160
Explanation: Set A: Starts with 1. $1\text{xxxxxxx}$. Count = $2^7 = 128$.\nSet B: Ends with 00. $\text{xxxxxx}00$. Count = $2^6 = 64$.\nIntersection $A \cap B$: Starts with 1 AND ends with 00. $1\text{xxxxx}00$. Count = $2^5 = 32$.\n$|A \cup B| = |A| + |B| - |A \cap B| = 128 + 64 - 32 = 160$.