# Digital Communications in FE Electrical

Digital communication in FE Electrical is the crucial exam topic per the NCEES® FE exam guidelines and syllabus. It is the founding block of our world as we see it today, instrumental in internal connectivity to satellite communication.

If you want to master digital communications for the Electrical FE Exam, this study guide will cover you. Let’s move towards further detail.

## Fundamentals of Digital Communications

In digital systems, signals and data are primarily presented and processed using the binary system, which is based on two discrete symbols, typically represented as 0 and 1. This binary representation forms the foundation of digital communication.

### Binary System and Digital Representation

To master communications for the Electrical FE Exam, let’s explore how binary and digital systems interconnect to enable digital communication.

#### Binary System

The binary system is the foundation of digital representation. It utilizes two symbols, 0 and 1, to represent information. All data in digital systems is ultimately represented as sequences of binary digits, known as bits.

##### Units/Objects of Data Representation in Binary System
• Bit (Binary Digit) – The fundamental unit of information in the binary system. It can take on one of two values: 0 or 1.
• Byte – A group of 8 bits, commonly used as the primary storage unit for data in most computer systems.
• Binary Number System – The binary number system represents numeric values using combinations of 0s and 1s.
• Binary Encoding – The process of representing characters, numbers, or other data using binary code. For example, ASCII (American Standard Code for Information Interchange) encodes characters into 7 or 8-bit binary codes.

#### Digital System

Digital system or digital data representation refers to how data is presented and stored in digital systems using the binary system. This can encompass various forms of data, including numbers, text, images, and more.

Analog-to-Digital Conversion (ADC): Converting continuous analog signals into discrete digital values. For example, when recording audio, analog sound waves are sampled and converted into digital signals.

Digital-to-Analog Conversion (DAC): Converting discrete digital values into continuous analog signals. This is used in applications such as playing digital audio through speakers.

#### Digital (Binary) Signals vs. Analog Signals

Digital and analog signals are two fundamental signals used in communication and data transmission. They differ in their representation, characteristics, and how they handle data. The table below outlines the key differences between binary and analog signals.

#### Interconversion Example of Analog and Binary

Let’s consider the interconversion of a decimal number into binary and vice versa.

##### Decimal to Binary Conversion

Step 1 – Start with the decimal number you want to convert.

Step 2 – Divide the decimal number by 2, and note the quotient and remainder.

Step 3 – Continue dividing the quotient by two and noting the quotients and remainders until the quotient becomes 0.

Step 4 – Write down the remainders in reverse order, as they were obtained. This is the binary representation.

Decimal Number: 45

Binary Representation: 101101

Let’s illustrate this process with the decimal number 45:

Step 1 – Decimal number to convert: 45

Step 2 – 45 ÷ 2 = 22 with a remainder of 1 (Quotient: 22, Remainder: 1)

Step 3 – 22 ÷ 2 = 11 with a remainder of 0 (Quotient: 11, Remainder: 0)

Step 4 – 11 ÷ 2 = 5 with a remainder of 1 (Quotient: 5, Remainder: 1)

Step 5 – 5 ÷ 2 = 2 with a remainder of 1 (Quotient: 2, Remainder: 1)

Step 6 – 2 ÷ 2 = 1 with a remainder of 0 (Quotient: 1, Remainder: 0)

Step 7 – 1 ÷ 2 = 0 with a remainder of 1 (Quotient: 0, Remainder: 1)

Now, write down the remainder in reverse order: 101101. So, the binary representation of the decimal number 45 is 101101.

##### Binary to Decimal Conversion

Step 1 – Converting binary to decimal involves a slightly different process, as you need to sum up the decimal values associated with each binary digit position.

Step 2 – Start from the rightmost (least significant) digit of the binary number.

Step 3 – Assign each binary digit position a weight starting from 2^0 (for the rightmost digit) and doubling for each position to the left (2^1, 2^2, 2^3, and so on).

Step 4 – Multiply each binary digit (0 or 1) by its corresponding weight.

Step 5 – Sum up the results from step 3 to get the decimal equivalent.

Binary Representation: 1101101

Decimal Number: 109

Let’s illustrate this process with the binary number 1101101:

Step 1 – Start from the rightmost digit, which is 1.

Step 2 – Assign weights from right to left: 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, and 2^6.

Step 3 – Multiply each binary digit by its weight:

1 * 2^0 = 1

0 * 2^1 = 0

1 * 2^2 = 4

1 * 2^3 = 8

0 * 2^4 = 0

1 * 2^5 = 32

1 * 2^6 = 64

Step 4 – Sum up the results: 1 + 0 + 4 + 8 + 0 + 32 + 64 = 109.

So, the decimal equivalent of the binary number 1101101 is 109.

#### Digital Communication Example – Mars Rover Communication Case Study

Let’s consider the case of a Mars rover, like NASA’s Curiosity rover, and its communication with Earth. In this scenario, digital signals play a crucial role in transmitting data collected by the rover back to Earth despite the inherent challenges of communicating over vast distances in space.

##### Digital Communication Hierarchy
1. Data Collection: The Mars rover collects various data types, such as images, environmental measurements, and scientific observations.
2. Analog Sensors: Many of the sensors on the rover generate analog signals as they respond to the physical environment.
3. Analog-to-Digital Conversion (ADC): To process the data, analog signals from sensors need to be converted to digital form. ADCs are used for this purpose. For instance, the rover’s camera captures images in analog form, which are converted to digital images for analysis.
4. Data Processing: The digital data is processed by the rover’s onboard computer systems to perform tasks like image analysis and data compression.
5. Digital Communication: To send data to Earth, the rover uses a digital communication system that encodes the collected information into digital signals, using various encoding techniques such as error-correcting codes.
6. Data Transmission: The digital signals are transmitted to an orbiter (satellite) orbiting Mars. The orbiter serves as a relay station.
7. Interplanetary Communication: The orbiter receives digital data, converts it to analog signals, and transmits them to Earth using radio waves. This analog-to-digital-to-analog conversion helps deal with the vast distances between Mars and Earth, as analog signals are less susceptible to errors over long distances.
8. Earth-based Reception: On Earth, the analog signals from the orbiter are received by ground-based radio telescopes.
9. Analog-to-Digital Conversion (ADC): The analog signals are then converted back to digital form using ADCs, allowing for the extraction of the original digital data.
10. Data Processing and Analysis: Once in digital form, the data is processed, analyzed, and interpreted by scientists and engineers on Earth.

Using digital signals on the Mars rover ensures data accuracy and integrity, and converting digital and analog signals during interplanetary communication helps overcome the challenges of transmitting data over vast distances in space.

This combination of technologies enables effective communication and data exchange between Mars rovers and Earth-based mission control centers.

### Pulse Code Modulation (PCM) and Digital Signal Processing (DSP)

#### Pulse Code Modulation (PCM)

Pulse Code Modulation (PCM) is a digital representation technique commonly used in signal processing to convert analog signals into discrete, quantized, and digitally encoded versions.

PCM is the basis for the transmission, storage, and manipulation of audio, video, and other analog data in digital systems. It is crucial in telecommunication, audio recording, and various digital communication systems.

##### How Does PCM Work?
1. Sampling: PCM begins with the process of sampling, where the analog signal is discretized at regular intervals (sampling rate). This results in a sequence of amplitude values sampled from the continuous signal.
2. Quantization: Following sampling, the sampled amplitudes are quantized. Quantization involves the assignment of discrete digital values to each sampled amplitude. The resolution of quantization is determined by the number of bits used, often referred to as the bit depth. A higher bit depth allows for more precise representation but requires more data bandwidth.
3. Encoding: The quantized values are then encoded into binary code using a binary numbering system. Each quantized value corresponds to a unique binary code word. The encoding typically uses two’s complement or sign-magnitude representation for signed data, depending on the application.
##### Things to Remember
• Bit Rate: The bit rate of a PCM signal depends on the sampling rate and the bit depth. A standard formula for calculating the bit rate is: Bit Rate (in bits per second) = Sampling Rate × Bit Depth.
• Signal-to-Noise Ratio (SNR): The SNR in a PCM system is a critical parameter that reflects the quality of the digitized signal. It measures the ratio of the signal power to the quantization noise power and is typically expressed in decibels (dB).
• Nyquist Theorem: The Nyquist theorem governs the sampling rate in PCM systems, stating that the sampling rate should be at least twice the highest frequency in the analog signal to avoid aliasing, a form of distortion.

#### Digital Signal Processing (DSP)

Digital Signal Processing (DSP) is a field of study and a technology domain that deals with the manipulation, analysis, and transformation of digital signals. It encompasses various applications, including filtering, compression, modulation, demodulation, and spectral analysis.

DSP leverages computational algorithms and mathematical techniques to process digital signals efficiently and accurately.

##### How Does DSP Work?
• Discrete-Time Signals: DSP operates on discrete-time signals, which are sequences of numerical values representing the sampled values of a continuous-time signal.
• Signal Transformation: DSP often involves applying mathematical operations, such as Fourier transforms, convolution, and filtering, to modify or analyze digital signals. These operations are typically implemented using algorithms.
• Filtering: Filtering is a fundamental DSP operation for noise reduction, signal enhancement, and extracting specific frequency components. DSP algorithms can implement various filter types, including low-pass, high-pass, band-pass, and notch filters.
##### Things to Remember
• Fast Fourier Transform (FFT): FFT is a critical DSP technique used to analyze the frequency content of signals. It efficiently computes the discrete Fourier transform, making it possible to perform spectral analysis and extract frequency domain information from time-domain signals.
• Digital Signal Processors (DSPs): DSPs are specialized microprocessors optimized for DSP operations. They are widely used in applications like audio processing, telecommunications, and image processing.
• Real-Time Processing: DSP is often employed in real-time systems where signals must be processed with low latency. This is crucial in applications like audio and video processing, where delays can be perceptible to humans.

*DSP can be implemented using specialized hardware, like digital signal processors (DSP chips), or software running on general-purpose processors. Hardware DSP accelerators offer real-time processing capabilities and are used in applications like audio processing and telecommunications.

Simply, PCM and DSP are intertwined technologies that enable the digitization and processing of analog signals for various applications. PCM converts analog signals into digital form.

Whereas DSP techniques are applied to analyze, modify, and enhance those digital signals to achieve specific objectives in fields such as audio processing, telecommunications, image processing, and more.

Further Reading: Transmission and Networking  in FE Electrical – Second Part of this FE Study Guide

### Conclusion

This topic of digital communications in FE Electrical involves a range of other essential topics and technical aspects. To study the next chapter of digital communication involving transmission and networking in FE Electrical, read our detailed study guide of this series.

For NCEES® FE Electrical exam preparation, we recommend checking out our comprehensive FE resources at Study for FE – Your go-to place for all things FE.

Licensed Professional Engineer in Texas (PE), Florida (PE) and Ontario (P. Eng) with consulting experience in design, commissioning and plant engineering for clients in Energy, Mining and Infrastructure.