**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**.