Digital Logic Circuits PDF

System Software and Computing Concepts CT123-3-1Ver: VDE Logic Gates  Topics we will cover Types of Gates Boolean algebra Truth Tables...

System Software and Computing Concepts CT123-3-1Ver: VDE Logic Gates  Topics we will cover Types of Gates Boolean algebra Truth Tables Logic Gate Design Module Code & Module Title Slide Title 2  Learning Outcomes At the end of this section, YOU should be able to: Define logic gates Discuss the characteristics of logic gates Explain functions of the AND, OR, NAND, NOR and Exclusive OR gates Design Circuits using Logic Gates Define Boolean Equations and Draw Truth Tables Module Code & Module Title Slide Title 3  Key Terms Integrated Circuit Switching Circuit Logic Gate Transistor Resistor Capacitor Karnaugh Map Truth-Table Boolean Module Code & Module Title Slide Title 4  Logic Gates: Introduction Computers – A Collection of Digital Switches At their core, computers are made up of switches that can turn on and off. These switches work together to process data using binary (0s and 1s). Integrated Circuits (ICs) Modern computers are built using tiny chips called Integrated Circuits (ICs) that contain thousands or even millions of switches. These chips make computers smaller, faster, and more ef cient. Specialized Functions of ICs Different ICs perform speci c tasks: ◦ CPU: Acts as the brain of the computer, performing calculations and executing instructions. ◦ Bus Interface: Manages communication between various parts of the computer. ◦ Memory Management Unit: Handles memory allocation and retrieval, optimizing how the system uses RAM and storage. Module Code & Module Title Slide Title 5 fi fi  Components of Integrated Circuits ICs consist of microscopic components like: ◦ Transistors: Serve as electronic switches or ampli ers, forming the core of logic gates. ◦ Resistors: Control the ow of current in the circuit. ◦ Capacitors: Store and release electrical energy. Transistors: The Building Blocks of ICs: A transistor is a tiny device that controls the ow of electricity. They are the foundation of modern electronics, enabling computers to perform logic operations. Fun Fact: Modern ICs can house more than 6.5 million transistors in an area smaller than half an inch squared. This incredible density is a result of advancements in nanotechnology and semiconductor manufacturing. Module Code & Module Title Slide Title 6 fl fl fi  Transistors Transistors are devices that control the movement of electrons, and consequently, electricity. They work something like a water faucet, not only do they start and stop the flow of a current, but they also control the amount of the current. Module Code & Module Title Slide Title 7  Resistors: A resistor is an electronic component that limits or regulates the flow of electric current in a circuit. It provides resistance, measured in ohms (Ω), and is used to control voltage, current, or divide power in electronic devices. Purpose: Resistors are components that control the ow of electricity by limiting the current in a circuit. Think of them like speed bumps for electric current—they slow it down but don’t stop it entirely. Resistor How They Work: Resistors resist the ow of electrons, converting some electrical energy into heat. Module Code & Module Title Slide Title 8 fl fl  Capacitors: A capacitor is an electronic component that stores and releases electrical energy in a circuit. It consists of two conductive plates separated by an insulating material (dielectric). Purpose: Capacitors are components that store and release electrical energy. Capacitor They act like small rechargeable batteries but can charge and discharge much faster. How They Work: Capacitors consist of two conductive plates separated by an insulating layer. When connected to a power source, they store energy by creating an electric eld between the plates. Module Code & Module Title Slide Title 9 fi  Dielectric De nition: The dielectric is the insulating material between the conductive plates. Purpose: It prevents the ow of current while allowing an electric eld to form, which stores energy. Example Materials: Common dielectrics include air, ceramic, glass, or Capacitor plastic. Conductive Plates De nition: These are the two layers of material (often metal) that hold opposite charges. Purpose: They store electrical charges. When a voltage is applied, one plate becomes positively charged, and the other becomes negatively charged, creating an electric eld. Example Materials: Aluminum or copper is often used for the plates. Module Code & Module Title Slide Title 10 fi fi fi fl fi  Logic 1. De nition in General: Logic is the art of reasoning based on strict principles to ensure conclusions are valid and consistent. For example, "Experience is a better guide than deductive logic" means practical understanding often leads to better outcomes than purely theoretical reasoning. 2. Logic in Computers: In electronics or computers, logic is a system of rules or principles that dictate how components are arranged and work together to perform speci c tasks ef ciently. These principles form the foundation of computer operations and processes. 3. Philosophical Logic: It refers to speci c systems of reasoning, like Aristotelian Logic, which introduced foundational ideas about proof, inference, and reasoning patterns. 4. Key Takeaway: Logic provides a framework for organizing thoughts, tasks, or systems in a structured Aristotle way. Father of Logic 5. Synonym: Reason. 6. Fun Fact: Aristotle, the Father of Logic, established formal methods to assess and validate reasoning, which still in uence modern thought and technology today. Module Code & Module Title Slide Title 11 fi fi fl fi fi  Algebra in Computer Logic 1. Boolean Algebra: ◦ Boolean algebra is the mathematical foundation for designing computer logic. ◦ It uses binary values (0 and 1) and logical operations like AND, OR, and NOT to perform computations and make decisions in digital circuits. 2. Transistors: ◦ Transistors are the building blocks that implement Boolean algebra in hardware. ◦ They act as electronic switches, controlling the ow of electricity in a circuit, representing binary values (0s and 1s). 3. Switches: ◦ Switches in digital circuits are either ON or OFF, which directly correspond to binary values: ON represents 1, and OFF represents 0. ◦ These states form the basis for all binary operations in computing. Module Code & Module Title Slide Title 12 fl  Algebra in Computer Logic 4. Logic Gates: ◦ Logic gates combine switches and transistors to perform logical operations. ◦ These gates (like AND, OR, NOT) are the core components used in computers to process information and make decisions. 5. Al-Khwarizm: ◦ Al-Khwarizm is known as the Father of Algebra, who developed fundamental principles of algebra in the 9th century. Al-Khwarizm: Father of Algebra ◦ His work laid the foundation for later advancements in mathematics and computing. Module Code & Module Title Slide Title 13  Digital Circuits Digital circuits process information using two types of logic: 1. Combinatorial Logic Key Idea: The output depends only on the current inputs. Think of it like a calculator: ◦ If you input numbers to add, the result depends only on the numbers you entered right now. ◦ Example: Add 2 + 3; the answer is 5. ◦ The answer doesn’t care about anything you did before. Uses: ◦ Performing arithmetic (e.g., addition or subtraction). ◦ Moving data from one place to another. ◦ Comparing values to make decisions (e.g., "Is A greater than B?"). Module Code & Module Title Slide Title 14  2. Sequential Logic Key Idea: The output depends on current inputs and past results. Think of it like a stopwatch: ◦ A stopwatch counts time continuously. ◦ The current reading depends on how long you've been running it (past results) and if you're still pressing the button (current input). This logic uses memory to store past results. Uses: counter Traf c Lights The sequence of traf c lights (Red → Green → Yellow → Red) depends on the previous light. It remembers the last state to decide the next one. Elevator Control System The elevator keeps track of its current oor (past state) and responds to input (e.g., which button was pressed). The next action depends on its current state and user input. Login System When logging into a website, the system tracks whether you are logged in (past state) or not. Your ability to access content depends on this state. Module Code & Module Title Slide Title 15 fi fi fl  What is a Counter in Sequential Logic? A counter is a simple example of sequential logic. It counts numbers in a sequence (e.g., 0, 1, 2, 3…). ◦ Example: ▪ At rst, it shows 0. ▪ When you give it an input (like a clock signal), it increases by 1: 0 → 1 → 2 → 3, and so on. Counters remember the last number they showed, so the next number depends on the previous result. Module Code & Module Title Slide Title 16 fi  Boolean Algebra What is it? Boolean Algebra is a branch of mathematics used in digital circuits to deal with values that have only two possible states: ◦ True/False ◦ On/Off ◦ Yes/No ◦ 0/1 (most common representation in computers). Why is it important? It forms the foundation of how computers and digital systems work, helping to design circuits and solve logical problems. Module Code & Module Title Slide Title 17  Boolean Logic Boolean Logic is a set of rules for working with Boolean constants and variables. It de nes how inputs combine to produce outputs in a logical way. 3 fundamental operations: AND, OR and NOT Truth Table What is it? A Truth Table is a table that shows all possible combinations of inputs and their corresponding outputs for a logical operation or circuit. Why use it? It helps us clearly understand how a circuit or Boolean expression behaves for every input. Module Code & Module Title Slide Title 18 fi  Boolean Operators AND - It has two inputs and one output. - The output is 1 (True) only when both inputs are 1 (True). - If even one input is 0 (False), the output will be 0 (False). Boolean Expression: - X= A.B or A ∧ B. Truth Table Logical Diagram Venn Diagram A B X = A.B 0 0 0 0 1 0 1 0 0 1 1 1 Module Code & Module Title Slide Title 19  Boolean Operators Real-Life Example Imagine you have a fan connected to two switches: 1. Switch A controls the power. 2. Switch B controls the fan blades. The fan will only turn ON (Output = 1) if both switches are ON (Inputs = 1). If one or both switches are OFF (Inputs = 0), the fan won’t turn on (Output = 0). Module Code & Module Title Slide Title 20  Boolean Operators OR (INCLUSIVE-OR) - It has two inputs and one output. - The output is 1 (True) if at least one input is 1 (True). - The output is 0 (False) only when both inputs are 0 (False). Boolean Expression: - Y= A + B. Truth Table Logical Diagram Venn Diagram A B X=A+B 0 0 0 0 1 1 1 0 1 1 1 1 Module Code & Module Title Slide Title 21  Boolean Operators Real-Life Example Think of a lamp connected to two switches: The lamp will turn ON (Output = 1) if either switch is ON or both are ON. The lamp will remain OFF (Output = 0) only if both switches are OFF. Module Code & Module Title Slide Title 22  Boolean Operators NOT - It has one input and one output. - The output is the opposite (inverse) of the input: - If the input is 1 (True), the output is 0 (False). - If the input is 0 (False), the output is 1 (True). Boolean Expression: - Y= ¬A or A′. Logical Diagram Truth Table Venn Diagram A Y = A’ 0 1 1 0 Module Code & Module Title Slide Title 23  Boolean Operators Real-Life Example Think of a light sensor: If the sensor detects light (Input = 1), it turns off the connected bulb (Output = 0). If there is no light (Input = 0), the bulb turns on (Output = 1). Module Code & Module Title Slide Title 24  Boolean Operators NAND - A NAND Gate (NOT AND Gate) is a digital logic gate that performs the inverse of an AND gate. - It outputs LOW (0) only when all its inputs are HIGH (1); otherwise, it outputs HIGH (1). - If all inputs are 1 (True), the output is 0 (False). - If any input is 0 (False), the output is 1 (True). Boolean Expression: - Y=(A⋅B)′ Logical Diagram Truth Table Module Code & Module Title Slide Title 25  Boolean Operators NOR - This gate is the combination of OR and NOT gates. - If all inputs are 0 (False), the output is 1 (True). - If any input is 1 (True), the output is 0 (False). Boolean Expression: - Y=(A+B)′ Logical Diagram Truth Table Module Code & Module Title Slide Title 26  Boolean Operators Exclusive-OR gate (XOR Gate) - This logic gate produces a high or logic 1 output when both of the inputs are dissimilar, otherwise it produces a logic 0 output. Boolean Expression: - Y=(A⋅B′)+(A′⋅B) or - Y= A⊕B Logical Diagram Truth Table Module Code & Module Title Slide Title 27  Boolean Operators Exclusive-NOR Gate (XNOR Gate) - The output of the XNOR gate is logic 1 when both the inputs are logic 1 or logic 0. - In other words, the output of the XNOR gate is logic 1 when both the inputs are the same. - For different inputs, the output of the XNOR gate is logic 0. Boolean Expression: - Y = A.B + A’.B' or - Y = A⊙B. Logical Diagram Truth Table Module Code & Module Title Slide Title 28  Boolean Operators Module Code & Module Title Slide Title 29  Boolean Algebra Operations Valid for INCLUSIVE-OR, AND, XOR – Associative A + ( B + C ) = ( A + B ) + C – Distributive A ( B + C ) = A B + A C – Commutative A + B = B + A DeMorgan’s Theorems – A + B = A B – A B = A + B Module Code & Module Title Slide Title 30  Gates and Combinatorial Logic: Sum of Two Single Binary Digits In combinational logic, many functions are de ned using Boolean equations, where the outputs depend only on the current inputs. For example, when adding two single binary digit numbers, we derive two outputs: 1. Sum (SUM) 2. Carry (CARRY) These are de ned as follows: Boolean Equations SUM: A⊕B (Exclusive OR) CARRY: A⋅B (AND) – Truth table for – Truth table for sum XOR carry AND Here: A and B are the inputs (binary digits: 0 or 1). ⊕ is the XOR operation. A B C A B C ⋅ is the AND operation. 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 Module Code & Module Title Slide Title 31 fi fi  Gates and Combinatorial Logic: Sum of Two Single Binary Digits Explanation with Gates 1. SUM (XOR): The XOR gate outputs 1 when exactly one of the inputs is 1. If both inputs are 0 or 1, the output is 0. 2. CARRY (AND): The AND gate outputs 1 only when both inputs are 1. Otherwise, it outputs 0. Practical Example: Suppose we add A=1 and B=1: SUM=A⊕B=1⊕1=0 (No sum output, as both bits are the same). CARRY=A⋅B=1⋅1=1 (There is a carry). These logic gates form the foundation of binary addition in circuits like Half Adders and Full Adders. Module Code & Module Title Slide Title 32  Computer Implementation Integrated Circuits Logical gates are implemented as integrated circuits (ICs) using transistors, diodes, resistors, and capacitors. Transistor Switches: The fundamental building blocks of ICs. They switch between high (1) and low (0) voltage levels to represent binary states. Types of ICs 1. Small-Scale Integration (SSI): Contains a few gates per chip. 2. Medium-Scale Integration (MSI): Contains up to hundreds of gates per chip (e.g., adders, multiplexers). 3. Large-Scale Integration (LSI): Contains thousands of gates per chip (e.g., processors, memory chips). 4. Very Large-Scale Integration (VLSI): Contains millions or billions of transistors integrated into a single chip. Module Code & Module Title Slide Title 33  Computer Implementation VLSI (Very Large-Scale Integration) De nition: VLSI refers to the process of creating complex integrated circuits by combining millions or billions of transistors onto a single chip. Applications: ◦ Microprocessors (e.g., CPUs and GPUs) ◦ Memory (RAM, ash storage) ◦ Application-speci c integrated circuits (ASICs) for tasks like image processing, machine learning, or network management. Key Features: High Performance: VLSI enables the design of fast and ef cient computational hardware. Compact Size: Combines large functionality into small physical space. Low Power Consumption: Optimized circuits reduce energy requirements. Module Code & Module Title Slide Title 34 fi fl fi fi  Selector or Multiplexer In electronics, a multiplexer (or selector) is an electronic device that chooses one input signal from multiple inputs and sends it to a single output line. It is like a switch that decides which input to forward. Key Points: Purpose: To handle multiple signals and send only one at a time to save space and resources. Use: Helps transmit more data efficiently over a network by sharing the same line for multiple inputs. Also called a data selector Module Code & Module Title Slide Title 35  Sequential Logic Circuits Unlike combinational logic, the output depends on both the current input and the previous state of the circuit. It "remembers" past information using memory elements. Flip-flop: are the building blocks of sequential circuits. They store a single bit of data, acting as memory for the circuit. State table: lists all possible combinations of inputs and previous states. It shows the resulting output and the next state of the circuit. Sequential logic used to build finite state machines, which control operations in devices. Essential for memory circuits, counters, registers, and timers in digital systems. Module Code & Module Title Slide Title 36  Example 1. Draw the truth table and write the Boolean Equation Inputs Outputs A B C D E Q 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 2. Draw a circuit that takes input from 3 doors and 1 0 1 0 0 0 raises an alarm whenever all 3 doors are open. 1 1 0 0 0 0 1 1 1 0 1 1 Module Code & Module Title Slide Title 37  Quick Review Questions Draw a circuit that takes input from 2 doors and raises an alarm whenever any door is open. Draw a circuit that takes input from 3 doors and raises an alarm whenever any 2 doors are open Module Code & Module Title Slide Title 38  Quick Review Questions Draw the truth table and write the Boolean Equation Module Code & Module Title Slide Title 39  Summary Logic functions provide ways to combine different digital signals or signals that can only take one of two possible levels, low level (0) and high level (1), based on the laws of Boolean algebra. These laws are applied using logic gates, which can be classified according to the number of available inputs. In a three state buffer, an enable signal is used to control whether the input signal is transferred toward the output or isolated from the output, which is then held in a high impedance state. A logic function can take four states: 0, 1, x and. A function with n variables may be represented by a truth table having n *#x002B; 1 columns and a maximum of 2 n lines. The design of multi level circuits is based on the factorization and decomposition of logic functions which are taken in their minimal form. Module Code & Module Title Slide Title 40 ‐ ‐ ‐ ‐  END Q&A Module Code & Module Title Slide Title 41  Next CPU & Memory Module Code & Module Title Slide Title 42