Lesson 2.1.2 & 2.1.3 Universal Gates & Logic Circuits PDF

**Lesson 2.1.2** **Lesson Objective:** - **Explains the use of universal gates; and** - **Describe the logic circuit using Boolean Expressions.** **UNIVERSAL GATES** **Universal gates** are fundamental components in digital circuits. They can be used to implement any Boolean function withou...

**Lesson 2.1.2** **Lesson Objective:** - **Explains the use of universal gates; and** - **Describe the logic circuit using Boolean Expressions.** **UNIVERSAL GATES** **Universal gates** are fundamental components in digital circuits. They can be used to implement any Boolean function without needing to use other types of gates. The two most common universal gates are **NAND** and **NOR** gates. **DEFINITION OF UNIVERSAL GATES** A **universal gate** is a type of logic gate that can perform any logical operation. This means that any complex circuit can be constructed using just universal gates. The versatility of these gates makes them essential in digital design. **NAND GATE OVERVIEW** The **NAND** gate is a combination of an **AND** gate followed by a **NOT** gate. Its output is false only when all inputs are true, making it a universal gate. **AND** gates can be used to create **NOT**, **AND**, and **OR** gates through proper configurations. **NOR GATE OVERVIEW**  The **NOR gate** is a combination of an **OR** gate followed by a **NOT** gate. Its **output is true** only when **all inputs are false**, making it another universal gate.Similar to NAND gates, NOR gates can also be configured to create other logic gates. **IMPORTANCE OF UNIVERSAL GATE** **Universal gates** allow for simpler circuit designs by reducing the variety of gates needed. They are cost-effective since fewer types of components can be used in manufacturing. Their ability to implement any logic function is **crucial in digital electronics.** **IMPLEMENTING BASIC GATES WITH NAND** - A **NOT gate** can be constructed by connecting both inputs of a NAND gate together. - An **AND gate** is created by connecting a NAND gate output to a NOT gate. - An **OR gate** can be formed by using two NAND gates in a specific configuration. **IMPLEMENTING BASIC GATES WITH NOR** - A **NOT gate** can be made by connecting both inputs of a NOR gate together. - An **OR gate** is created by feeding the outputs of two NOR gates into a NOT gate. - An **AND gate** can be formed through the use of two NOR gates in a specific arrangement. **PRACTICAL APPLICATIONS** Universal gates are widely used in programmable logic devices and FPGAs. They form the backbone of many digital systems, including microprocessors and memory devices. Their flexibility allows for rapid prototyping and testing of digital circuits. **COMPARISON BETWEEN NAND AND NOR** Both **NAND** and **NOR** gates are equally powerful as universal gates. The choice between using NAND or NOR often depends on design preferences or specific applications. In practice, NAND gates are generally more common due to their simpler implementation in CMOS technology. **CONCLUSION** Understanding universal gates is essential for anyone studying digital logic design. Their ability to create any logical function simplifies the design process significantly. Mastery of NAND and NOR gates opens up numerous possibilities in electronic circuit design. Sources; Mano, M. M. (2017). Digital Logic and Computer Design. Prentice Hall. Roth, C. H. (2018). Fundamentals of Logic Design. Cengage Learning. **Lesson 2.1.3** **LOGIC CIRCUIT** **BASIC CONCEPTS OF LOGIC GATES** At their essence, logic circuits, sometimes referred to as **digital logic circuits**, are used to perform complex computations in digital systems such as computers and calculators. **DEFINITION;** A **logic circuit** can be defined as an electrical circuit that executes logical operations on one or more binary inputs to produce a single binary output. They operate based on Boolean algebra principles, which are grounded in the truth values true and false, often represented as 1 and 0, respectively. **Logic circuits** are critical in CPU microarchitecture and cores to undertake tasks such as computation, encoding, multiplexing, and memory interfacing. They also play a significant role in developing hardware like ALUs (Arithmetic Logic Units). Every logic circuit contains multiple components, but the essential ones are the logic gates. Now, let\'s have an in-depth look at these components and their varieties. **Logic circuits** are broadly classified as either combinational or sequential. **Combinational logic circuits\'** outputs depend solely on the current inputs, while **sequential logic circuits\'** outputs depend on both the current inputs and the history of past inputs. **Logic circuits** serve as tools for representing, processing and manipulating information in digital systems, transforming binary inputs or Boolean information into outputs based on their specified logic rules. **WHAT ARE BOOLEAN EXPRESSIONS?** **Boolean Expressions** are algebraic forms that represent logical relationships. They consist of **variables** that can take values of true or false combined using operators such as **AND, OR,** and **NOT**. These expressions allow us to model and simplify logic circuits effectively. **SIMPLYING BOOLEAN EXPRESSIONS** Simplification of **Boolean expressions** is crucial for optimizing logic circuits. Techniques like **De Morgan\'s Theorems** and **Karnaugh maps** help reduce complexity while maintaining functionality. Simplified expressions lead to fewer gates and enhanced circuit performance. **TYPES OF LOGIC GATE** **Logic gates** are the building blocks of logic circuits. The most common types include **AND**, **OR** and **NOT** gates. Each gate performs a specific logical function, and their combinations create more complex circuits. Understanding these gates is essential for decoding logic. **TRUTH TABLES EXPLAINED** **Truth tables** are tools used to represent the output of logic gates based on their inputs. They show all possible combinations of input values and the corresponding output. By analyzing truth tables, we can derive the Boolean expressions for specific logic circuits. **CONCLUSION: THE IMPORTANCE OF LOGIC CIRCUITS** Understanding **logic circuits** through **Boolean expressions** is vital for anyone in electronics. It enables better design, efficiency, and problem-solving in digital systems. As technology advances, mastering these concepts will remain essential for future innovations. **ACTIVITY NO. 2.1.2 & 2.1.3** **Name:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_Grade & Level:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Date:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **I. Fill in the blank/s to complete each statement.** 1\. A \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ can be defined as an electrical circuit that executes logical operations on one or more binary inputs to produce a single binary output. 2\. The most common types include \_\_\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_\_\_and \_\_\_\_\_\_\_\_\_\_\_\_gates. 3\. The NAND gate is a combination of an \_\_\_\_\_\_\_\_\_\_\_\_gate followed by a \_\_\_\_\_\_\_\_\_\_\_\_gate. 4\. \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ are algebraic forms that represent logical relationships. 5\. \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ are the building blocks of logic circuits. 6\. \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ are fundamental components in digital circuits. 7\. \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ are tools used to represent the output of logic gates based on their inputs. 8\. Logic circuits, sometimes referred to as \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 9\. The NOR gate is a combination of an \_\_\_\_\_\_\_\_\_\_\_\_ gate followed by a \_\_\_\_\_\_\_\_\_\_\_\_ gate. 10\. They consist of \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_that can take values of true or false combined using operators such as AND, OR, and NOT.