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Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Lecture



Basics of digital electronic technology.

Logical and digital devices
Mathematical apparatus
• Number systems (decimal, binary, hexadecimal) - a way to display a number by a set of numbers;
• Algebra of logic;
• The unit of information in digital systems is bit (BInary digiT).
The bit can take two values ​​- zero and one.
• A group of eight bits is byte.
1 byte = 8 bits is a binary word;
16 bits = 2 bytes - machine word;
4 bits = ½ byte - tetrad.

Number systems

• The decimal number system uses digits from the natural number series.
• DEM uses binary number system, where only two values ​​0 and 1 machine language are used.
• Hexadecimal s / c. more compact.

Binary number system
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Conversion from binary to decimal.

00010100 = 27 • 0 + 26 • 0 + 25 • 0 + 24 • 1 + 23 • 0 + 22 • 1 + 21 • 0 + 20 • 0 = 16 + 4 = 20

Conversion from decimal to binary is done by dividing by 2.

Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Binary Number Decimal Number Hexadecimal Number

Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Logic algebra

• Each specific set of variable values ​​can be considered as an n-bit binary code, therefore the number of such sets.
• Any Boolean function of variables can be given by a truth table, or analytically in the form of structural formulas.

Rules and relations in the algebra of logic:
The switching and combining laws of mathematics are applicable.

A + B = B + A

AB = BA

A (B + C) = AB + AC

ABC + AC + AB + BC = AC (B + 1) + B (A + C)

Logical elements

The binary logic element is an electronic circuit, the output state of which is described by one of the main Boolean functions.
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

The logical element "NOT"
element notation truth table and structural formula

Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Logical element "OR"
element notation truth table and structural formula
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

"OR-NOT" - element (inverse disjunction)
element notation truth table and structural formula
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

"And" - logical multiplication (conjunction)
element notation truth table and structural formula
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

"AND-NO" - element (inverse conjunction)
element notation truth table and structural formula
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Exclusive OR
element notation truth table and structural formula
Basics of digital electronic technology. Number Systems Logic Algebra Logic Elements AND OR NOT Combined Logic Elements

Combined logic elements

Elements “NOT”, “AND”, “OR”, etc. are combined to implement more complex logical functions: encoders, decoders, multiplexers, demultiplexers, half adders, etc.

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Digital devices. Microprocessors and microcontrollers. computer operating principles

Terms: Digital devices. Microprocessors and microcontrollers. computer operating principles