An online store uses 6-bit binary sequences to identify each unique item for sale. The store plans to increase the number of items it sells and is considering using 7-bit binary sequences. Which of the following best describes the result of using 7-bit sequences instead of 6-bit sequences?
Responses
2 more items can be uniquely identified.
2 more items can be uniquely identified.
10 more items can be uniquely identified.
10 more items can be uniquely identified.
2 times as many items can be uniquely identified.
2 times as many items can be uniquely identified.
10 times as many items can be uniquely identified.
10 more items can be uniquely identified.
2 times as many items can be uniquely identified.
To answer this question, we need to understand the concept of binary sequences. In binary, each bit can have two possible values: 0 or 1. So, a 6-bit binary sequence can represent 2^6 (2 raised to the power of 6) different combinations, which equals 64 unique values. Similarly, a 7-bit binary sequence can represent 2^7 different combinations, which equals 128 unique values.
Now, let's compare the two options given:
- Using 7-bit sequences instead of 6-bit sequences will result in 2 more items being able to be uniquely identified.
- Using 7-bit sequences instead of 6-bit sequences will result in 10 more items being able to be uniquely identified.
- Using 7-bit sequences instead of 6-bit sequences will result in 2 times as many items being able to be uniquely identified.
- Using 7-bit sequences instead of 6-bit sequences will result in 10 times as many items being able to be uniquely identified.
Among these options, the correct answer is: 2 times as many items can be uniquely identified.
This is because each additional bit doubles the number of possible combinations. So, by adding one more bit (going from 6-bit to 7-bit sequences), the number of unique values doubles.