Digital Circuits and Logic Design: A Simplified Guide

Name: Digital Circuits and Logic Design: A Simplified Guide
Rating: 4.6 (8 reviews)

Digital Circuits, Logic Gates, Combinational Circuits, Sequential Circuits, Karnaugh maps, Boolean Algebra

Created bySaqer Alhloul, PhD

Last updated 10/2024

English

English [Auto],

What you'll learn

Converting Decimal to Binary numbers and vice versa
Perform binary arithmetic operations
Building digital circuits using logic gates
Simplify circuits using Boolean algebra
Optimize digital circuits using Karnaugh maps
Building combinational digital circuits
Building sequential circuits

Course content

10 sections • 79 lectures • 9h 40m total length

Introduction1:07
Explore the fundamentals of digital circuits with practical applications, in a concise course that breaks down complex topics into simple, easily digestible lessons.
Course Learning Objectives2:27
Convert decimal to binary and vice versa, perform binary arithmetic, and build digital circuits with logic gates, optimize with Karnaugh maps, and design combinational and sequential circuits using flip-flops.
Simulation tool used in the course1:36
Install and use Logisim, a simulation tool for digital circuits, to access basic logic gates and workspace components for hands-on experimentation throughout the course.

Decimal Numbering System4:49
Explore how digital circuits communicate in binary, then relate binary to the decimal system by using the base concept and base ten, with digits 0-9.
Decimal Numbers Representation: Sum of Weights Method7:41
Explain how decimal numbers are represented as sums of weights using powers of ten; for example, 354 = 3×10^2 + 5×10^1 + 4×10^0, preparing for binary mapping.
Binary Numbering System8:00
Explore the binary numbering system, using two digits 0 and 1 and base two, including negative representations. Learn counting with binary digits, parentheses notation, and how binary relates to decimal.
Converting a Binary Number to a Decimal Number: Sum of Weights Method7:46
Explore binary to decimal conversion in digital circuits with the binary expansion method, using two to the powers and msb/lsb concepts, illustrated by 110₂ equals six.
Converting a Binary Number to a Decimal Number: Repetitive Division Method11:18
Learn to convert decimal numbers to binary using the long division method, applying repetitive division by two and recording the least significant bits. Terminate when the quotient reaches zero.
Counting in Binary using the Sum of Weights Method4:07
Explore the sum of weights method for converting decimals to binary and revising binary counting; with n digits you can count up to 2^n - 1, and preview truth tables.
Converting a Decimal Number to Binary using the Sum of Weights Method8:49
Learn to convert decimal numbers to binary with the sum of weights method: find n, list weights from 2^{n-1} to 2^0, and assign 1s and 0s to form binary.
Counting in Binary (A Systemic Approach)10:09
Explore a systematic approach to counting in binary using the sum of weights, build binary representations for 0–15, and uncover bit-pattern principles for efficient truth tables.
Binary Numbers Addition6:03
Master binary addition by applying simple carry rules for zero and one, and verify results by converting binary sums to decimal.

Introduction to Logic Gates5:08
Learn how digital circuits use logic gates to transform binary inputs into outputs. Explore simple gates (not, and, or) and complex gates (nand, nor, xor, xnor) and related two-input models.
Binary Numbers and Voltage Levels5:06
Represent binary numbers as electrical signals, with zero volts for off and five volts for on, in digital circuits using transistors such as BJT and MOS.
The NOT Gate (Inverter)9:00
Explore how the not gate inverts a single input, using the symbol and the logical expression f(a)=a_bar, and illustrate with a truth table for off (0) and on (1).
The AND Gate10:38
Explore the and gate, a boolean multiplication with two inputs (a and b) and output f, illustrated by symbol, logical expression, and truth table using a lamp analogy.
The OR Gate8:55
Explore the or gate as boolean addition with two inputs A and B, using its symbol and truth table to show output when at least one input is on.
Practical Applications Design Process2:13
Apply the design process to a smart home control circuit by turning a problem statement into a boolean expression, wiring logic gates, and validating with a truth table and simulator.
A Smart Home Lighting System Design I4:28
Design a smart home automatic lighting system that turns on a secondary light when the primary is off or when on with no motion, using inputs A and B.
A Smart Home Lighting System Design II6:39
Build a truth table for smart home circuit by applying a' and b', then a and b', and combine with or to form f = a' or (a and b').
A Smart Home Lighting System Design III12:03
Design a smart home lighting circuit from f = not A or A and not B using an inverter, and gate, and or gate, and verify with a truth table.

The NAND Gate7:49
Explore the nand gate by decomposing it into an and gate followed by an inverter, and compare symbol, logical expression, and truth table representations.
The NOR Gate3:59
Learn how the nor gate, a two-input complex gate built from or and not gates, inverts the or output to a high only when both inputs are off.
The XOR and XNOR Gates12:38
Explore the xor and xnor gates, their symbols and truth tables, and see how to build xor from and, not, and or gates, and explain detecting difference or equality.
Industrial Safety System Design I10:47
Design an industrial safety alarm using a two-input digital circuit that monitors machine status and temperature. Use truth tables and or, xor, and nor gates to build the logic.
Industrial Safety System Simulation4:32
Design an industrial safety system simulation using A and B inputs with OR and XOR gates, wiring, and a probe to trigger alarms, then apply Boolean algebra for simplification.

Boolean Algebra Basic Theorem14:42
Learn how Boolean algebra simplifies digital circuits by applying basic laws: x or zero equals x, and x and zero equals zero.
Idempotent, Complementary, Involution and Commutative Laws13:55
Explore idempotent, complementary, involution, and commutative laws in Boolean algebra, showing that x or x equals x, x and x equals x, and x or not x equals 1.
Associative Laws6:28
Explore the associative laws for and and or operations in boolean algebra, showing how multi-input expressions can be implemented with two-input gates and simplified circuits.
First and Second Distributive Laws14:18
Explore the first and second distributive laws in Boolean algebra, showing how to simplify circuits, derive standard SOP and POS expressions, and prepare for practical circuit standardization.
Demorgan's Theorem7:08
Master the De Morgan theorem in Boolean algebra by breaking the bar and distributing it across variables, with sign changes. Verify equivalence with truth tables and simplify circuits.
Industrial Safety System Optimization using Boolean Algebra12:25
Apply boolean algebra to optimize an industrial safety system by simplifying a circuit that monitors machine status and temperature, achieving a nand gate implementation.
Industrial Safety System Optimization using Boolean Algebra Simulation2:42
Apply boolean algebra to optimize an industrial safety circuit by replacing a nor gate, exclusive or, and or with a nand gate, and verify equivalence in a logic simulator.

Standard Logical Expressions, SOP and POS Introduction8:39
Learn standard processes for boolean expressions by exploring standard sum of products and standard product of sums, De Morgan's laws, and truth table verification.
Categorizing Boolean Expressions7:18
Categorize logical expressions by identifying whether they are sum of products, product of sums, or general expressions, and recognize standard SOP and standard POS forms.
Converting Boolean Expressions to a SOP I6:12
Standardize logical expressions to simplify truth tables and circuit design by converting them into standard sums of products using De Morgan's theorem, distributive laws, and the complement rule.
Converting Boolean Expressions to a SOP II4:56
Explore standardizing sum of product expressions, identify sop, pos, or general forms, fill missing variables using the complementary rule, apply distributive laws, and remove redundancy.
Building a Truth Table using a SOP9:46
Learn to build a truth table from a standard SOP, apply the Morgan transformation, and determine the A and B input combinations that yield ones, then verify the table.
Getting a SOP expression from a Truth Table5:00
Identify ones in the truth table and build product terms using inputs and their complements, then sum the products to obtain a standard sop expression, including examples like xor.
Building a Digital Circuit using a SOP expression9:25
Learn to build a digital circuit from a standard SOP expression using two variables, applying standardization and wiring inverted and noninverted lines to and gates and or gates.
A Security System Design8:51
Explore a practical security system design using motion and pressure sensors, truth tables, and SOP to derive a simple or gate implementation.
Standard Product of Sums (POS)5:59
learn to convert a two-variable expression to a standard product of sums by applying de Morgan's laws, the second complementary law, and distributive laws to include all variables.
Building a Truth Table from a POS6:46
Standardize the POS, identify binary inputs that make every term zero, and assign f=0 for those cases to build the truth table; apply complementary and distributive laws for missing variables.
Creating a POS expression from a Truth Table6:25
derive a standard pos from a truth table by circling zeros, analyzing or gates, and inverting inputs to produce zero outputs, yielding a product of sums expression.
Creating a Digital Circuit using a POS expression8:33
Learn to build a digital circuit from a pos by standardizing, applying de morgan, and using inverted and non-inverted a and b lines to three or terms feeding an and.
Choosing a SOP or a POS6:30
Learn to choose sop or pos from a given truth table by counting ones versus zeros, derive the corresponding terms, and compare gate efficiency and nand/nor implementations.

An Introduction of K-Maps7:25
Explore the k-map for two variables to visually simplify boolean expressions, map outputs from the truth table to four cells, and connect to sop and pos guided circuit design.
Translating logical expressions to a K-map9:54
Translate logical expressions into k-maps by standardizing to sop or pos, building truth tables, and reducing expressions via map-based grouping.
K-Maps Neighborhoods7:18
Explore k maps neighborhoods to form minimal expressions by grouping adjacent horizontal or vertical cells with the same value, maximizing neighborhoods up to four in two-variable maps, and avoiding diagonals.
Simplifying Logical Expressions using a K-map11:12
Learn to simplify logical expressions with k-maps by mapping truth tables, establishing optimum neighborhoods, and minimizing expressions in SOP or POS.

The Half Adder circuit11:57
Explore combinational circuits and the half adder, which sums two binary inputs A and B into a sum and a carry out, using xor and and gates.
Implementing Full Adders using Half Adders6:59
Design a full adder from two half adders to accept a carry in and output a sum and carry out for binary addition.
Simulation of Half Adders and Full Adders12:41
Simulate half adders and full adders with a circuit simulator. Build a full adder from two half adders and an or gate, test inputs, and verify sum and carry outputs.
Encoders Our way to Talk to Digital Circuits7:22
Explore how an encoder translates four button presses into binary signals, producing two outputs (A1 and A0) representing MSB and LSB, using a truth table and OR operations.
Encoders Simulation5:07
Simulate a four-by-two encoder using four push buttons, produce two outputs, and label them as A1 and A0; test, verify, and save modular combinational circuit designs for reuse.
Decoders, The Way Digital Circuits Talk to us6:15
Explore decoders as the converse of encoders, converting binary digits into seven-segment display signals and enabling digital circuits to talk back to us.
Decoders Design I10:39
Design and analyze decoder circuits that map binary inputs to a single active output, using active high decoders with and gates and inverters, and active low decoders with nand gates.
2X4 Decoders Design6:04
Explore a two-by-four active-high decoder that maps two inputs to four one-hot outputs with inverted and non-inverted lines, and note larger decoders (3x8, 4x16, 5x32) and half adder applications.
Implementing a Half Adder using a Decoder6:12
Implement a half adder with a two by four decoder by building a truth table, using or gates to derive sum and carry out.
A Decoder Simulation6:32
Simulate a two-by-four decoder in Logisim to verify the designed logic, then implement a half adder using the decoder outputs. Explore inputs, inverters, and gates, and test all input combinations.
A 7 Segment Decoder Design10:45
design a 7-segment decoder that maps binary inputs to seven outputs a–g for digits 0–3, using truth tables and k-maps to derive and implement the logic.
A 7 Segment Decoder Design II7:35
Design and analyze the seven-segment decoder outputs b, c, d, e, f, and g using boolean algebra, SOP and POS methods, reinforced by truth tables.
A 7 Segment Decoder Simulation5:23
Simulate the seven segment decoder, build a subcircuit, connect inputs a and b, use xnor and or with inverters, and verify the truth table with binary tests.
The Multiplexer Circuit Design9:25
Explore how a multiplexer selects one of multiple inputs using a control line, demonstrated with a two-by-one mux feeding a single screen from front yard or back yard cameras.
A 4X1 Multiplexer Design4:54
Design a four-by-one mux with four inputs and two select lines, using inverted and non-inverted paths within a sum of products structure.
Multiplexer Circuit Simulation4:08
Explore a two-by-one multiplexer through a logisim simulation, wiring two inputs, one switch, and building the circuit from two and gates and an or gate.

The SR Latch an Intro5:57
Learn how sequential circuits differ from combinational circuits and how memory devices latch a binary value using the SR latch with set and reset inputs.
The SR Latch circuit Analysis12:22
Construct a sr latch from two nand gates with set and reset inputs and feedback. Learn the valid set, reset, no-change, and invalid states through step-by-step truth-table analysis.
The SR Latch Characteristics Table3:36
The SR Latch optimization to reduce power consumption2:32
Discover how to achieve the no-change state of an sr latch when s and r are both zero by adding two inverters to the nand inputs, producing q and qn.
Controlled (Gated) SR Latch7:53
Discover how a gated SR latch uses a control input to enable or disable S and R, turning it into a memory element with active high or active low operation.
The D Latch6:36
Transform an sr latch into a one-input memory by feeding d to set and inverted d to reset, forming the d latch that stores a bit with q and q̄.
The Controlled D Latch6:29
Build a controlled D latch using and gates and a control signal, explore active high and active low configurations, and connect to SR latch behavior and D flip-flop basics.
The D Flip Flop6:43
Explore how a D flip flop uses a D latch driven by a clock to store data via positive and negative edge triggering in sequential circuits.
The D Flip Flop Characteristics Table4:31
Explore how a d flip flop, a clock-driven d latch with inputs d and clock and outputs q and q naught, uses positive or negative edge triggering.
Synchronous Counter Design I8:39
Explore synchronous counter design using flip flops, including next state tables, clocked d flip flops, and the path from synchronous circuits to finite state machines.
Synchronous Counter Design II9:40
design a synchronous 2-bit counter that counts 0 to 3 using two d flip-flops, transition tables, and k-maps, with d0 = q0' and d1 = q1 xor q0.
A Synchronous Counter Simulation3:44
This lesson demonstrates building a synchronous counter with d flip-flops, an xor circuit, and a seven-segment display to count from 0 to 3, including clock wiring and feedback.

Requirements

basic algebra

Description

In this comprehensive course, you'll gain a solid foundation in digital circuits, starting with an introduction to the decimal and binary numbering systems. You'll learn how to perform binary arithmetic, a crucial skill for understanding digital logic. From there, we dive into the world of logic gates, where you'll explore how these fundamental building blocks operate and how to analyze their behavior in different circuits.

Next, we move on to Boolean algebra, a powerful mathematical tool used to simplify and manipulate logic expressions. You'll also learn the process of standardization to convert logic expressions into standard forms like sum-of-products (SOP) and product-of-sums (POS). Following this, we introduce Karnaugh Maps (K-Maps), a visual technique to further simplify logic circuits, making them more efficient and easier to design.

As the course progresses, you'll explore combinational logic circuits, which use logic gates to perform specific tasks without memory elements. Finally, the course wraps up with an introduction to sequential circuits, where memory elements come into play, and you'll learn how to design circuits with timing considerations.

To ensure a straightforward and accessible learning experience, this course introduces all topics using two input variables. Once these concepts are well understood, they can be easily extended to handle multiple variables.

Throughout the course, you'll apply these concepts to practical examples and simulations, ensuring you can confidently design and analyze digital circuits in real-world scenarios such as security and industrial safety systems and many other applications.

Please note that students under the age of 18 may only access this course if a parent or guardian purchases and manages the account. All course materials are intended for adult supervision to ensure a guided and responsible learning experience for younger students.

Who this course is for:

College and high school students who are studying digital circuits and seeking a clear, structured approach to learning the fundamentals.
Hobbyists and DIY enthusiasts interested in understanding the building blocks of digital electronics, whether for personal projects or expanding their knowledge.
Learners new to digital circuits who may feel overwhelmed by complex concepts and are looking for simplified, practical explanations.
Students taking a digital circuits course who want additional support to grasp difficult topics and need a more digestible approach.
Professionals or engineers seeking a quick refresher on digital circuit fundamentals to strengthen their foundational knowledge.

Digital Circuits and Logic Design: A Simplified Guide

What you'll learn

Explore related topics

Course content

Introduction3 lectures • 5min

Numbering Systems9 lectures • 1hr 9min

Simple Logic Gates & Digital Circuits9 lectures • 1hr 4min

Complex Logic Gates5 lectures • 40min

Boolean Algebra7 lectures • 1hr 12min

Standardizing Boolean Expressions13 lectures • 1hr 34min

Karnaugh Maps (2 Variables Only)4 lectures • 36min

Combinational Digital Circuits16 lectures • 2hr 2min

Sequential Circuits12 lectures • 1hr 19min

Concluding Remarks1 lecture • 1min

Requirements

Description

Who this course is for: