39 mark for review a store uses binary numbers to assign a unique binary sequence to each item in its…

39 mark for review a store uses binary numbers to assign a unique binary sequence to each item in its inventory. what is the minimum number of bits required for each binary sequence if the store has between 75 and 100 items in its inventory? a 5 b 6 c 7 d 8

39 mark for review a store uses binary numbers to assign a unique binary sequence to each item in its inventory. what is the minimum number of bits required for each binary sequence if the store has between 75 and 100 items in its inventory? a 5 b 6 c 7 d 8

Answer

Explanation:

Step1: Recall binary number formula

The number of unique values that can be represented with $n$ bits is $2^n$.

Step2: Test different values of n

For $n = 5$, $2^5=32$. Since $32<75$, 5 bits is not enough. For $n = 6$, $2^6 = 64$. Since $64<75$, 6 bits is not enough. For $n = 7$, $2^7=128$. Since $75\leq128$ and $128 > 100$, 7 bits is sufficient. For $n = 8$, $2^8 = 256$, which is also sufficient but we want the minimum number of bits.

Answer:

C. 7