Question

The bit rate for a signal which has a sampling rate of $8\,kHz$ and where $16$ quantisation levels have been used is:
A. $32000\,bit\,{\sec ^{ - 1}}$
B. $16000\,bit\,{\sec ^{ - 1}}$
C. $64000\,bit\,{\sec ^{ - 1}}$
D. $72000\,bit\,{\sec ^{ - 1}}$

Answer 1

In computing and digital communications, bits is the most basic and smallest unit of information storage, the sampling rate in computers are the measurements of the number of taken sample in each second and this is nothing but a frequency and hence its SI units is Hertz. Quantisation represents the number of chosen samples for a finite set of levels, we will use the concept of number of quantisation in order to find the bit range from the given data in question.

Formula used:
If $n$ is the number of bits per sample than the total number of quantisation levels is calculated by formulas a,
Number of quantisation level is $= {2^n}$
The bit rate of the given sample is calculated by using the formula
Bit range $=$ Sampling rate $\times$ Number of bits per sample.

Complete step by step answer:
According to the question, we have given that the number of quantisation levels is equal to $16$. Let $n$ is the number of bits per sample then using the formula;
Number of quantisation level is $= {2^n}$ we have,
$16 = {2^n}$
$\Rightarrow {2^n} = {2^4}$
With the same base of two, compare the powers we get,
$n = 4$
Now, we have given that the sampling rate is equal to $8\,kHz$ using the formula of
Bit range $=$ Sampling rate $\times$ Number of bits per sample
We get it.
Bit range $= 8000 \times 4$
Bit range $= 32000\,bit\,{\sec ^{ - 1}}$

Hence, the correct option is A.

Note: It should be remembered that, the basic unit of conversion as $1\,kHz = 1000\,Hz$ and a bit range represents the total number of distinct values a sample can store, other most common and highly used units of computer storage are KB MB which are read as Kilobytes and Megabytes.