the cars manufacturer is considering a software update that will use an 8 - bit binary number to represent…

the cars manufacturer is considering a software update that will use an 8 - bit binary number to represent the cars speed. which of the following best describes the result of making this change?\na the 8 - bit format can represent 2 times as many speeds as the 7 - bit format.\nb the 8 - bit format can represent 8 times as many speeds as the 7 - bit format.\nc the 8 - bit format can represent 16 times as many speeds as the 7 - bit format.\nd the 8 - bit format can represent 64 times as many speeds as the 7 - bit format.

the cars manufacturer is considering a software update that will use an 8 - bit binary number to represent the cars speed. which of the following best describes the result of making this change?\na the 8 - bit format can represent 2 times as many speeds as the 7 - bit format.\nb the 8 - bit format can represent 8 times as many speeds as the 7 - bit format.\nc the 8 - bit format can represent 16 times as many speeds as the 7 - bit format.\nd the 8 - bit format can represent 64 times as many speeds as the 7 - bit format.

Answer

Explanation:

Step1: Recall bit - representation formula

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

Step2: Calculate number of values for 7 - bit and 8 - bit

For a 7 - bit binary number, the number of values it can represent is $2^7$. For an 8 - bit binary number, the number of values it can represent is $2^8$.

Step3: Find the ratio

We want to find the ratio $\frac{2^8}{2^7}$. Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{2^8}{2^7}=2^{8 - 7}=2$.

Answer:

A. The 8 - bit format can represent 2 times as many speeds as the 7 - bit format.