Digital Logic Circuit PDF

Digital Logic Circuit Logic Gate Mak(Prof. KIM) A303 010 6201 2453 [email protected] 1  Today's lecture table of contents Binary Logic AN...

Digital Logic Circuit Logic Gate Mak(Prof. KIM) A303 010 6201 2453 [email protected] 1  Today's lecture table of contents Binary Logic AND, OR, NOT Gate NAND, NOR Gate XOR, XNOR Gate 2 What is a Binary Logic? Binary logic is a system of mathematical logic that deals with variables that have two distinct values: true (1) and false (0). It forms the foundation of digital electronics and computer science. Here are the key aspects of binary logic: 1. Binary Variables: These variables can only take on one of two values, typically represented as 0 and 1. 2. Logical Operations: Binary logic uses operations such as AND, OR, and NOT to manipulate binary variables. 3. Truth Tables: These tables are used to represent the output of a logical operation for all possible input combinations 4. Applications: Binary logic is used in designing digital circuits, including computer processors, memory devices, and various other digital systems 3  Binary Logic Definition of Binary Logic Binary logic consists of binary variables and a set of logical operations. The variables are designated by letters of the alphabet, such as A, B, C, x, y, z, etc, with e ach variable having two and only two distinct possible values: 1 and 0. Three basic logical operations: AND, OR, and NOT. 4 Binary Logic Positive Logic Definition: In positive logic, a higher voltage level represents a logical ‘1’ (true), and a lower voltage level represents a logical ‘0’ (false). Example: In a 5V system, 5V might represent a logical ‘1’, and 0V might represent a logical ‘0’. Usage: This is the most common convention used in digital circuits, including most computer systems and microcontrollers Negative Logic Definition: In negative logic, a higher voltage level represents a logical ‘0’ (false), and a lower voltage level represents a logical ‘1’ (true). Example: In the same 5V system, 5V would represent a logical ‘0’, and 0V would represent a logical ‘1’. Usage: Negative logic is less common but can be useful in certain types of circuits and applications where this convention simplifies the design 5 What is a Logic Gate? A logic gate is an electronic device that performs a Boolean function, meaning it takes one or more binary inputs (0s and 1s) and produces a single binary output. These gates are the fundamental building blocks of digital circuits and are used in various electronic devices and systems. Here are some common types of logic gates: 1. AND Gate: Outputs true (1) only if all inputs are true. 2. OR Gate: Outputs true if at least one input is true. 3. NOT Gate: Outputs the opposite of the input (also known as an inverter). 4. NAND Gate: Outputs false (0) only if all inputs are true (the opposite of AND). 5. NOR Gate: Outputs true only if all inputs are false (the opposite of OR). 6. XOR Gate: Outputs true if an odd number of inputs are true. 7. XNOR Gate: Outputs true if an even number of inputs are true (the opposite of XOR). These gates can be combined in various ways to perform complex operations and are essential in the design of digital systems like computers, calculators, and more. 6 AND, OR, NOT Gates Truth Tables, Boolean Expressions, and Logic Gates AND OR NOT x y z x y z x z 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 z=x y=xy z=x+y z = x = x’ x x x y z y z z  AND, OR, NOT Gates Logic gates Graphic Symbols and Input-Output Signals for Logic gates: Fig. 1.4 Symbols for digital logic circuits 8 Fig. 1.5 Input-Output signals for gates AND, OR, NOT Gates Logic gates Graphic Symbols and Input-Output Signals for Logic gates: Fig. 1.6 Gates with multiple inputs 9 Overview : Logic Gates, NOT gate ( ~ 05:17, Skip the back part) 10 AND gate (14:13) 5:28 11 OR gate (12:39) : can be omitted 12 Buffer Gates Buffer Gate is used to amplify a weak signal source. It is designed to take an input signal and produce an output signal that is identical to the input signal, but with a higher current capacity. A F F=A 13 Buffer Gates 3-state Buffer Gate E E A F A F High-impedance (or Hi-Z) is a state in When a pin is in a high-impedance which a circuit node allows only a state, it is effectively disconnected from relatively small amount of current the circuit and does not drive the signal through per unit of applied voltage at line to either a high or low state that point Since the logical variable E is primarily a variable used to indicate whether a circuit is enabled or not, circuit designers recommend not to use it. 14 NAND, NOR Gates NAND Gate A F B F = AB = A  B A F B Most semiconductors make all circuit components only NAND gates in order to take advantage of circuit size reduction and operating speed when designing semiconductors. 15 NAND, NOR Gates NOR Gate A F B F = A+ B A F B 16 NAND gate, NOR gate (10:50) 17 NAND, NOR gates = Universal Gate NAND and NOR Gates are called Universal Gates because AND, OR and NOT gates can be implemented & created by using these gates. NAND Gate Implementations NOR Gate Implementations Universal Gate : NAND gate (08:55) 19 Universal Gate : NOR gate ( ~ 08:19, skip the back part) 20 XOR Gates XOR gate(Exclusive-OR gate) : odd function A F = A  B = AB + AB B F 21 XOR Gates XOR gate(Exclusive-OR gate) 3-input A F = A B C B F C 22 Attention!!!! The logical expression on page 22 is mathematically fine But the computer performs binomial operations, so be careful with odd functions with inputs of 3, 5, 7,..... A simple explanation of this in the truth table is as follows. If you need to describe a logical expression in this case, you can replace one of the logical operators with an even number of operators. 23 Attention!!!! Note: You will understand if you take a lecture on the expression of the logical expression. XNOR Gates XNOR gate(Exclusive-NOR gate) : even function A F = AB + AB B F = A B =A B A F B 25 XNOR Gates XNOR gate(Exclusive-NOR gate) 3-input F = A B C A B F =A B C C 26 XOR gate 27 XNOR gate (14:13) 28 Electrical Characteristics of the Gate Gate propagation delay time(When the input signal passes through the logic gate, the output signal appears a little later.) 5V 50% 0V 5V 50% 0V tPHL tPLH 29 Electrical Characteristics of the Gate Fan Out : Indicates the maximum number of output terminals that can be connected from one gate to the input from another gate. Fan In : Means the number of stages that can be accessed as input to a single gate. 30 Thank you! See you next time. Mak(Prof. KIM) A303 010 6201 2453 [email protected] 31