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# Bits Calculator + Online Solver With Free Steps

The **Bits Calculator** is an online tool that helps you find the sample size of a given signal in the form of bits. The length of a continuous-time signal, when converted to discrete time, is called its **sample size**.

It is an excellent **calculator** for students and engineers to find the sample size of the signals.

## What Is the Bits Calculator?

**The Bits Calculator is an online calculator that enables you to determine the sample size of the signals based on their sampling and quantization rates.**

**Sampling** is the fundamental concept of signal processing as it converts a continuous signal into a discrete signal. Most of the devices use data in digital form.

That’s why it has many applications in the fields of **telecommunication**, **engineering**, and **audio processing**. It is not easy to find the exact sample size as for this you need to have basic knowledge about sampling and do some calculations.

But you can quickly **solve** these problems using the **Bits Calculator**. This calculator performs state of art by providing accurate and precise results.

## How To Use the Bits Calculator?

To use the **Bits Calculator**, you are required to enter the time, sampling, and quantization rates of your problem in their respective spaces.

The user can easily navigate through the calculator due to its simple interface. The step-by-step **procedure** to use this calculator is given below.

### Step 1

Enter the **time** for sampling in the first box. There are three options available for the time that are hours, minutes, and seconds. Select according to your problem.

### Step 2

Then put the **sampling rate** at which you want to sample the signal in its box. This can vary from one application to another.

### Step 3

Also, enter the **quantization rate** in the third box.

### Step 4

Now click the **Submit **button to find out the result. The result is the **sample size** in the form of the number of **bits**. Also, it represents the obtained size in multiple **units**.

## How Does the Bits Calculator Work?

The bits calculator works by calculating the **sample size **of a digital signal for the given quantization and sampling rate and finding the sample size in bits.

This calculator determines the sample size by the following formula:

**Sample size = Time * Sampling rate * Quantization**

The above formula requires sampling rate, time and quantization hence there should be knowledge about these concepts.

### Sampling and Sampling Rate

Sampling is the process of measuring the instantaneous values of a** continuous-time** signal in a **discrete **time. It is the chunk of data that is taken from the continuous data.

Sampling is used to convert a continuous-time signal into a** discrete **time signal. The small value of measurement of the continuous-time signal is called a** sample**.

The **sampling frequency **or sampling rate is the number of samples that are acquired in one second. The reciprocal of the sampling rate is called the **sampling period**.

\[\text{Sampling rate} = f_s= 1/T_s\]

Where $f_s$ is the sampling frequency and $T_s$ is the sampling time.

When converting the analog signal into the digital signal the sampling rate should be accurate because the information in the signal should neither be lost nor get overlapped. This accuracy is determined by the sampling theorem.

### Sampling Theorem

The **sampling theorem **says that “the signal can be exactly reconstructed if its sampling rate is** greater than twice** the signal’s maximum frequency.” This theorem is also known as the** Nyquist theorem**.

This sampling rate is called the** Nyquist rate** by which there is no loss or overlap of the signal. The sampling theorem leads to two types of sampling one type is under-sampling and the other is over-sampling.

The **under-sampling** is that sampling in which the continuous signal is sampled** lower **rate than its Nyquist rate. When a bandpass signal is under-sampled, the samples of a low frequency are unable to differentiate from the higher frequency samples.

When the signal is sampled at a** higher** rate than its Nyquist rate that signal is called **over-sampled**. It is used to diminish distortion and noise effects from the signals that are obtained by practical analog to digital converters.

### Quantization

Quantization is the process of** mapping **a continuous signal into a discrete signal. This method selects some points on the analog signal and then joined these points to culminate the value into a near-stabilized value.

The discrete and countable levels in which the analog signal is quantized those levels are known as **quantization levels**. The device that is used to perform quantization is called **Quantizer**.

The output status of the quantizer is determined by the number of **quantization levels** used in quantization. The output of the quantizer is discrete quantized levels.

The amplitudes of these levels are known as **representation** levels or **reconstruction **levels. The distance between two adjoining reconstruction levels is termed **step-size** or **quantum**.

There are two types of quantization that are explained below.

#### Uniform Quantization

The quantization in which quantization levels are **uniformly** distributed is called **uniform quantization**. The analog amplitude remains constant all over the signal in this quantization because every step size shows a constant amount of amplitude.

#### Non-Uniform Quantization

The type of quantization in which the quantization levels are **non-uniformly** spaced is known as** non-uniform quantization**. The relation between quantization levels is **logarithmic**.

The analog signal goes through the compressor that implements a logarithmic function on the analog signal.

## Solved Examples

Here are some solved examples by the calculator. Let’s explore them.

### Example 1

Suppose an audio signal is sampled at 44KHz for an hour with a quantization rate of 8 bits per sample. What will be the sample size of the signal?

### Solution

The size of the sample will be:

**1.267 x $10^{6}$ bits**

#### Unit Conversion

The sample size is given in different units below. The capital letter **‘B’** represents byte and the letter ‘**b’** represents the bits.

**0.1584 GB, 158.4 MB, 1.584 x $10^{8}$ bytes, 1.276 Gb, 151.1 MiB**

### Example 2

Consider the following sampling details of a continuous signal. Determine the sample size

**Time = 30 mins, Sampling Rate = 88.2 Khz, Quantization Rate = 16 bits/sample**

### Solution

The number of bits required to store the sample is:

**2.54 x $10^{9}$ bits**

#### Unit Conversions

**0.3175 GB, 317.5 MB, 3.175 x $10^{8}$ bytes, 2.54 Gb, 302.8 MiB**