PC & MATH

Binary logic deals with variables that take discrete values ​​and with operators that

take on logical meaning. While any logical element (variable) or condition is needed

always have a logical value (0 or 1), there must also be ways

to combine different logical signals or conditions to provide one

logical result. For example, consider the logical statement: “If I e

turn on the key on the wall, the light will come on. “At first glance, this looks like

an accurate statement. However, if we look at some other factors, we realize that there is

more than that. In this example, a more complete statement would be: “If I e

turn on the switch and the lamp is functional and electricity is present, the light will

it lights up. ”If we look at these two statements as logical expression and usage

logical terminology, we can formulate the first statement in:

Light = Switch

This means nothing more than the light will follow the Switch action, so

that when the key is up (ON / true / 1) the light will also be ON / true / 1. We

on the other hand, if the key is down (OFF / false / 0), the light will also be OFF

/ false / 0. Looking at the second version of the statement, the formulation would be

a little more complex:

Light = Switch AND Bulb AND Power

MAIN OPERATORS AND PLATES

When it comes to logic circuits (like computers), we don’t just have to

deal with logical functions; but we also need some symbols of

special to define these functions in a logical scheme. There are three

basic logical operations, from which all functions of

others, however complex. These functions are named AND, OR, and NOT. each

of them there is a special symbol and a clearly defined behavior.

The basic blocks that form a computer (physically) are called logic gates or

only the gate. Gates are basic circuits that have at least one (and usually several) inputs and exactly one output. The input and output values ​​are the logical values ​​TRUE (1) and FALSE (0). In computer architecture it is common

use 0 for false and 1 for true. The gates have no memory. The output value depends

only by the actual value of the inputs. A useful way to describe

the relationship between the input values ​​of the ports and the output is the table of that

stalkers. In a truth table, the value of each output is tabulated for each

possible combination of input values. Three main logic gates as well as three

the main logical operations are AND, OR and NOT. AND, OR and NOT otherwise

are also called logic operators. Ports are the foundations of building a logic circuit. Their physical production is i

varied, so we can mention: logic gates built with

diode (DL), logic gates built with transistors and resistors (RTL), gates

logic built with diodes and transistors (DTL), CMOS ports, etc. Everything

these types of ports have their advantages and disadvantages either side by side

economically as well as functionally. Thanks to the problems one encounters

engineer, selects the right gate to produce logic circuits. One of the main goals when building digital circuits is to find ways

to make them as simple as possible. This constantly requires that

complex logical expressions are reduced to simpler expressions which

produce the same results in all possible conditions. The expression with e

simply then it can be applied with a smaller and simpler circuit, which

on the other hand it saves the price of unnecessary gates, reduces the number of gates

necessary and reduces the power and amount of space required by those gates.

Simple circuits are cheaper to produce, consume less energy and

work faster than complex circuits.

One tool to reduce logical expressions is the mathematics of logical expressions,

presented by George Boole in 1854 and known today as logical algebra (Boolean

Algebra). The rules of Boolean algebra are simple and straightforward, and

can be applied to any logical expression. Simplified expression derived from

the application of the rules of logical algebra can be easily tested if it gives the same

output with unspoken expression, using a truth table for each

combination of inputs.

Bull’s Algebra is a mathematical system for manipulating variables that can

have one of two possible values ​​(0 or 1). Buleane (logical) expressions are obtained

performing operations with logical operators. – Common actions are:

NOT, AND and OR. Logical F function F i n binary variables x1, x2 … xn is called the law according to which each

one of the binary combinations of n variables is given a value in correspondence

0 or 1. The function can be given in algebraic table form (truth table), or

in the form of a combinatorial network (in logic gates). Combinatorial logic circuit

consists of the logical gate, the results of which (output) are determined at any time

directly from the current combination of inputs regardless of the input of

preceding. A combinatorial logic circuit performs a specific processing of

information, processing which can be logically expressed by a logical function

and logical operators. A combinatorial circuit is a generalized port. we

generally such a circuit has more inputs and outputs. Such a circuit can always

is built as a community of smaller combinatorial circles, each with exactly one

exit. For this reason, we will study combinatorial circuits with exactly one output.

To determine the exact mode of operation of a combinatorial circuit, can

use different methods, such as logical expressions or truth tables.

As mentioned above, a truth table is a complete presentation of

all possible combinations of input values, each related to the value of

exit.

Below is an example of a solution to a problem with a truth table:

PROBLEM

Three keys command the ignition of a lamp. At least two keys must be ON

for the lamp to light up. In any other case the lamp stays off.

ANALYSIS

Since a combinatoric logic circuit will be built, the circuit will be expressed by

a logical function using the bulge algebra. Then the keys will

are represented as binary values, as well as the result (key ON -> 1, key OFF-> 0

light bulb -> 1, light bulb -> 0). Marking the three keys with the variables x, y.

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