Example of using a DHT11 sensor with a PIC16F1704. We use Timer2 to handle the timing part.

pic16f1705_dht11.c

/******************************************************************************/
/* This example is running on a PIC16F1704 @ 4Mhz INTOSC                      */
/* To use it you need to configure your OSC and other things.                 */
/* The SIGNAL pin of the DHT11 is wired to the RA4 pin                        */
/* We add a little margin for all timing (~)                                  */
/* Some information about the DHT11 :                                         */
/* http://akizukidenshi.com/download/ds/aosong/DHT11.pdf                      */
/******************************************************************************/
#include <xc.h>

#include <stdio.h>
#include <stdint.h>

void readDHT11() {
    // Declaration & Initialisation
    int i, j = 0;
    uint8_t data[5] = {0x00, 0x00, 0x00, 0x00, 0x00};

    // Hardware initialisation
    ANSELAbits.ANSA4 = 0;

    // 1/ Start condition (We ask him if he's there and for data in the same time)
    TRISAbits.TRISA4 = 0; // RA4 as output
    RA4 = 0; // RA4 put LOW
    __delay_ms(20); // LOW for ~18uS
    RA4 = 1; // RA4 put HIGH
    __delay_us(30); // HIGH for ~20/~40uS
    TRISAbits.TRISA4 = 1; // RA4 as input

    // 2/ Acknowledge (Guess if he understand our demand)
    TMR2 = 0;
    TMR2ON = 1;
    
    // Should be LOW for 80uS (if it took more than 100uS then the sensor is not reachable)
    while(!PORTAbits.RA4) {
        if(TMR2 > 100) {
            printf("DHT11 timeout error\n");
            return;
        }
    }

    TMR2 = 0;
    // Should be HIGH for 80uS (if it took more than 100uS then the sensor is not reachable)
    while(PORTAbits.RA4) {
        if(TMR2 > 100) {
            printf("DHT11 timeout error\n");
            return;
        }
    }
    
    // 3/ Read data sent by the DHT11 (5bytes == 40bits == 5x8 bits) (He respond & When are listening)
    for(i = 0; i < 5; i++) {
        for(j = 0; j < 8; j++) {
            while(!PORTAbits.RA4); // LOW 50uS

            // Reset and restart timer2
            TMR2 = 0;
            TMR2ON = 1;

            while(PORTAbits.RA4); // HIGH 30-70uS

            TMR2ON = 0;

            // If it was high for more than 30uS then it's a 1, otherwise it's a 0
            if(TMR2 > 30)
                data[i] |= 1<<(7-j);
        }
    }

    // Print out the data
    printf("%d %d %d %d %d\n", data[0], data[1], data[2], data[3], data[4]);
}

void main(void)
{
    // Configure Timer2
    T2CON = 0b0;  // Prescaler 1:1 / Postcaler 1:1 / Turned Off
    PR2 = 255;  // Maximum Value (not used anyway)

    // Read DHT11 every 0.5s
    while(1) {
        readDHT11();
        __delay_ms(500);
    }
}