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В папке библиотеки находится папка examples с примером её использования, пример рабочий, но если полностью скопировать файл в другое место (папка со скетчами), то он перестаёт работать и Дуина пишет следующее:

Вот ссылка на Яндыкс Диск (библиотека): https://yadi.sk/d/7Txb9QHq3Hoe5x

Вот код: 

// Example testing sketch for various DHT humidity/temperature sensors
// Written by ladyada, public domain

#include "DHT.h"

#define DHTPIN 2     // what pin we're connected to

// Uncomment whatever type you're using!
//#define DHTTYPE DHT11   // DHT 11 
//#define DHTTYPE DHT22   // DHT 22  (AM2302)
#define DHTTYPE DHT21   // DHT 21 (AM2301)

// Connect pin 1 (on the left) of the sensor to +5V
// NOTE: If using a board with 3.3V logic like an Arduino Due connect pin 1
// to 3.3V instead of 5V!
// Connect pin 2 of the sensor to whatever your DHTPIN is
// Connect pin 4 (on the right) of the sensor to GROUND
// Connect a 10K resistor from pin 2 (data) to pin 1 (power) of the sensor

// Initialize DHT sensor for normal 16mhz Arduino
DHT dht(DHTPIN, DHTTYPE);
// NOTE: For working with a faster chip, like an Arduino Due or Teensy, you
// might need to increase the threshold for cycle counts considered a 1 or 0.
// You can do this by passing a 3rd parameter for this threshold.  It's a bit
// of fiddling to find the right value, but in general the faster the CPU the
// higher the value.  The default for a 16mhz AVR is a value of 6.  For an
// Arduino Due that runs at 84mhz a value of 30 works.
// Example to initialize DHT sensor for Arduino Due:
//DHT dht(DHTPIN, DHTTYPE, 30);
//-----------дисплей-----------
#include <TM74HC595Display-old.h>
int SCLK = 7;
int RCLK = 6;
int DIO = 5;
TM74HC595Display disp(SCLK, RCLK, DIO);
unsigned char LED_0F[29];
//--------дисплей-------
void setup() {
  Serial.begin(9600); 
  Serial.println("DHTxx test!");
 
  dht.begin();
}

void loop() {
  // Wait a few seconds between measurements.
  delay(2000);

  // Reading temperature or humidity takes about 250 milliseconds!
  // Sensor readings may also be up to 2 seconds 'old' (its a very slow sensor)
  float h = dht.readHumidity();
  // Read temperature as Celsius
  float t = dht.readTemperature();
  // Read temperature as Fahrenheit
  float f = dht.readTemperature(true);
  
  // Check if any reads failed and exit early (to try again).
  if (isnan(h) || isnan(t) || isnan(f)) {
    Serial.println("Failed to read from DHT sensor!");
    return;
  }

  // Compute heat index
  // Must send in temp in Fahrenheit!
  float hi = dht.computeHeatIndex(f, h);

  Serial.print("Humidity: "); 
  Serial.print(h);
  Serial.print(" %\t");
  Serial.print("Temperature: "); 
  Serial.print(t);
  Serial.print(" *C ");
  Serial.print(f);
  Serial.print(" *F\t");
  Serial.print("Heat index: ");
  Serial.print(hi);
  Serial.println(" *F");
}