Compuertas Lógicas

Introduction to Logic Gates

What are Logic Gates?

• Logic gates are elements that take one or more binary input signals and produce a binary output based on these inputs.

• They operate with two states: 0 (off, no signal) and 1 (on, presence of signal).

• Logic gates perform binary logical operations such as addition, subtraction, multiplication, negation, inclusion, and exclusion.

Importance of Logic Gates

• They are fundamental components in digital electronics and crucial for designing automation systems.

AND Gate Functionality

Characteristics of the AND Gate

• The AND gate requires a minimum of two inputs; it outputs 1 only if all inputs are present (equal to 1).

• The truth table visualizes the output state based on different input combinations.

Truth Table Analysis

• For input A = 0 and B = 0, the output is 0.

• For input A = 0 and B = 1, the output remains 0.

• When both inputs A = 1 and B = 1, the output is finally equal to 1.

Boolean Equation Representation

Deriving Output from Inputs

• The Boolean equation for an AND gate is expressed as Out = A * B.

• This equation helps construct the truth table by evaluating all possible input combinations.

Tools for Understanding Outputs

• Two main tools to determine outputs: truth tables and Boolean equations.

Contact Language Representation

Contact Configuration for AND Gate

• In contact language representation for an AND gate, there are two normally open contacts arranged in series.

Circuit Implementation Example

• In a simple circuit with a power source and a bulb:

• Input values represent contact states: zero when not pressed (open), one when pressed (closed).

• Bulb status indicates output: off equals zero; on equals one.

Practical Examples of Input Combinations

Analyzing Different States

• If both contacts A and B are open (not pressed), the bulb remains off (output is zero).

Various Input Scenarios:

• A = 0 & B = 1: Bulb stays off since energy cannot flow through an open contact.

• A = 1 & B = 0: Similar outcome; energy flows but cannot reach the bulb due to one open contact.

• A = 1 & B = 1: Both contacts closed allow energy flow to light up the bulb (output equals one).

Logic Gates Explained

Introduction to Logic Gates

• The logical gate, also known as the OR function, operates with a minimum of two inputs. The output is 1 if at least one input is present.

Truth Table for Logical Gate

• The truth table shows that when both inputs A and B are 0, the output is 0. If A is 0 and B is 1, the output becomes 1.

• When A is 1 and B is 0, the output remains 1. Lastly, if both A and B are 1, the output stays at 1.

Representation of Logical Gate

• This logical gate can be represented mathematically as: Output (Out) = Input A + Input B.

• For example, with inputs A = 0 and B = 0, Out = 0 + 0 = 0; with A = 0 and B = 1, Out = 0 + 1 = 1.

Binary Operations in Logic Gates

• Results from binary operations can only yield outputs of either 0 or 1. Thus, when calculating with binary numbers like (A + B), results will always conform to this rule.

Contact Language Representation

• In contact language representation for logic gates, two normally open contacts are installed in parallel to represent inputs A and B.

Understanding NOT Gate

Functionality of NOT Gate

• The NOT gate has a single input that inverses its signal; it converts a signal of input value '0' into '1', and vice versa.

Truth Table for NOT Gate

• The truth table indicates that if the input is '0', then the output becomes '1'. Conversely, if the input is '1', then the output turns into '0'.

Mathematical Representation of NOT Gate

• Mathematically expressed as: Output (Out) = ¬A (negation). This means if A equals zero then Out equals one.

Contact Language Representation for NOT Gate

• In contact language representation for a NOT gate using a normally closed contact: If not pressed (state zero), energy flows to light up a bulb; if pressed (state one), energy flow stops.

Exploring NAND Gate

Definition of NAND Gate

• The NAND gate combines an AND operation followed by negation. Its name derives from "NOT AND".

Symbolism of NAND Gate

• It features two inputs (A & B) and one output (Out). Unlike an AND gate symbol which lacks negation indication at its output port.

Logical Gates: Understanding AND and NOR Functions

The AND Gate Logic

• The AND gate outputs 1 when both inputs A and B are 0, 0 and 1, or 1 and 0; it outputs 0 only when both inputs are 1.

• The truth table for the AND gate shows that its outputs are the negation of the corresponding outputs from a NOT operation.

• The logical equation representing this gate is expressed as out = NOT (A * B), where the output is derived from the product of inputs A and B.

• For input combinations, if A = 0 and B = 0, then out equals NOT(0*0), which results in an output of 1.

• When both inputs are set to 1, the output becomes NOT(1*1), resulting in an output of 0.

Representation in Contact Language

• The AND gate can be represented using two normally closed contacts arranged in parallel.

• In scenarios where both contacts remain unpressed (A = 0, B = 0), energy flows through to light a bulb, yielding an output of 1.

• If only contact B is pressed (A = 0, B = 1), energy still flows through contact A since it remains closed; thus, the bulb lights up with an output of 1.

• Pressing only contact A also allows energy flow through contact B leading to an output of one as well.

• However, pressing both contacts opens them up preventing any energy flow to the bulb resulting in an output of zero.

Introduction to NOR Gate Logic

• The NOR gate functions as a combination of a NOT operation following an OR function.

• It features two input ports (A and B) with one single output. Its symbol differs from that of an OR gate by having a small circle indicating negation at its output port.

Truth Table for NOR Gate

• For input values where both A and B equal zero, the NOR gate produces an output of one.

• When either input is set to one while the other remains zero (A = 0 & B = 1 or A = 1 & B = 0), the result will be zero for each case respectively.

• This relationship indicates that all outputs from a NOR gate are essentially negations compared to those from an OR gate's truth table.

Logical Equation for NOR Gate

• The logical expression for this configuration can be written as out = NOT (A + B) which helps derive results consistent with its truth table.

• For instance, if A equals zero and B equals one (out would yield NOT(01)), resulting in zero after summation followed by negation.

Logic Gates and Their Functions

Understanding Basic Logic Gate Operations

• The initial state of the circuit is described, where both inputs A and B are 0. In this case, energy flows from the source to the bulb, resulting in an output of 1.

• When input A is not pressed (0) but input B is pressed (1), the circuit opens at contact B, preventing energy flow to the bulb. Thus, the output becomes 0.

• If only input A is pressed (1), it opens while B remains closed. Energy cannot reach the bulb, leading to an output of 0.

• When both contacts A and B are pressed (1), they open and block energy flow to the bulb as well. Consequently, the output remains 0.

Exclusive OR Gate Functionality

• The exclusive OR gate (XOR) outputs a 1 if exactly one of its inputs is 1; it excludes cases where both inputs are high.

• The truth table for XOR shows that when both inputs are low or high, the output is 0; when one input is high and the other low, the output is 1.

Truth Table Comparisons

• Comparing XOR with standard OR gates reveals that their outputs differ only when both inputs are high; XOR outputs 0 while OR outputs 1.

• The mathematical representation for XOR can be expressed as: textOutput = (neg A cdot B) + (A cdot neg B) .

Evaluating Output Combinations

• For input combination A = 0 and B = 0: Both negations yield zeroes leading to an overall output of zero.

• For combination A = 0 and B = 1: The first part evaluates to one while second yields zero; thus, total output equals one.

• With inputs A = 1 and B = 0: This results in a final evaluation yielding an output of one due to active negation interactions.

Circuit Representation in Contact Language

• The XOR gate can be represented using contact arrangements where normally open/closed configurations dictate energy flow based on pressing conditions.

• Describes how interconnections between normally open and closed contacts affect overall circuit behavior during simultaneous presses on different contacts.

Logic Gates and Their Functions

Understanding Circuit Behavior with Logic Gates

• The energy flow in a circuit is affected by open and closed contacts. When the energy encounters an open contact, it cannot continue to the light bulb, while a closed contact allows the current to flow, resulting in an output of 1.

• In another scenario, pressing one contact closes it while opening another. If the energy flows through the lower line and meets an open contact, it cannot reach the bulb; however, if it flows through the upper line where a closed contact exists, it can illuminate the bulb.

• When both contacts are pressed simultaneously, one closes while another opens. The energy may flow through either line but will ultimately be blocked by an open contact on both paths, leading to no power reaching the bulb and thus an output of 0.

Introduction to XOR and XNOR Logic Gates

• The XNOR gate functions as a combination of XOR followed by NOT. It has two input ports and one output port. The small circle at the output indicates negation compared to standard XOR gates.

• The truth table for XNOR shows that when both inputs are 0 (A = 0, B = 0), the output is 1. For other combinations (A = 0 & B = 1 or A = 1 & B = 0), outputs are consistently different from those of XOR gates.

Truth Table Analysis

• Comparing truth tables reveals that outputs for XNOR are negated versions of those from XOR:

• A = 0 & B = 0 → Output is 1

• A = 0 & B = 1 → Output is 0

• A = 1 & B = 0 → Output is also 0

• A = 1 & B = 1 → Output returns to being 1.

• This relationship highlights how each combination's result flips between these two types of gates based on their definitions.

Mathematical Representation of XNOR Gate

• The logical function for XNOR can be expressed mathematically:

• textOutput = (neg A cdot neg B) + (A cdot B)

This equation helps derive results consistent with its truth table across all input combinations.

• For instance:

• With inputs A and B both equal to zero:

(neg(0))(neg(0)) + (0)(0) rightarrow (1)(1)+ (0)=1.

Further Combinations in Truth Table Evaluation

• Evaluating further combinations:

• For A = 0 and B = 1:

(neg(0))(neg(1)) + (0)(1)rightarrow (1)(0)+(0)=0.

• Continuing this process for other values confirms consistency with expected outputs:

• For A = 1 and B = 0:

(neg(1))(neg(0)) + (1)(0)rightarrow (0)(1)+(00)=00.

Practical Application in Circuit Design

• In practical terms, implementing an XNOR gate involves using normally open and normally closed contacts arranged such that pressing them alters their states appropriately within a circuit design context.

Understanding Electrical Contacts and Their Combinations

Overview of Contact Combinations

• The first scenario describes a closed contact that leads to an open contact, preventing energy flow towards the bulb. As a result, the output remains zero.

• In the second combination, pressing one contact closes it while another opens. Energy cannot flow through either path due to open contacts, leading again to a zero output.