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Test BME280 on Sensor Booster Pack

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From the datasheet and  it's Guide Manual http://www.ti.com/lit/ug/slau666b/slau666b.pdf
BME280 has a slave address: 0x77;

To control it we need to config several register as below:

Control Humidity Register (ADDR: 0xF2) Default 0x00 not activate
Control Measure Register (ADDR: 0xF4) Default 0x00 not activate
           b[7:5]: control temperature measurement
           b[4:2]: control pressure measurement
           b[1-0]: Control IC mode
                         00: sleep mode
                         01,10: force mode
                         11: normal mode
Control filter Register (ADDR: 0xF5) Default 0x00
           b[7:5]: control standby time
           b[4:2]: control  IRR filter
           b[0]   : config SPI in 3 wires ('1') /4 wires ('1')

default ID:  ADDR: 0xD0   Value: 0x60 (96)

This example to test read humidity from IC
Setup I2C in CC2640:

    int32_t        hum;
    uint16_t       adc_H;
    uint8_t         id;
    //uint8_t         pow;
    uint8_t         txBuffer[2];  //BME280 require ADDR Register>> Command Register
    uint8_t         rxBuffer[8];
    I2C_Handle      i2c;
    I2C_Params      i2cParams;
    I2C_Transaction i2cTransaction;

    I2C_init();
    I2C_Params_init(&i2cParams);
    i2cParams.bitRate = I2C_400kHz;
    i2c = I2C_open(Board_I2C_TMP, &i2cParams);
    if (i2c == NULL) {
        Display_printf(display, 0, 0, "Error Initializing I2C\n");
        while (1);
    }
    else {
        Display_printf(display, 0, 0, "I2C Initialized!\n");
    }

Config control register
    /* Common I2C transaction setup */
    i2cTransaction.writeBuf   = txBuffer;
    i2cTransaction.writeCount = 1;
    i2cTransaction.readBuf    = rxBuffer;
    i2cTransaction.readCount  = 1;

     i2cTransaction.slaveAddress = BME280_ADDR;
    //READ ID device
    txBuffer[0] = 0xD0;
    if (I2C_transfer(i2c, &i2cTransaction))
    {
        //light = (rxBuffer[0] << 8) | (rxBuffer[1]);
        id = rxBuffer[0];
        Display_printf(display, 0, 0, "Device ID: %d (C)",
                        id);

    }

// Configuration for measuring
    i2cTransaction.writeCount = 2;
    txBuffer[0] = 0xF5;
    //  |b7    |b6     |b5      |b4     |b3     |b2     |b1     |b0     |
    //  | time to sleep         |filter                 |not    |'1':SPI 3,'0':SPI 4|
    txBuffer[1] = 0x2C; //0x2Ct_sb =  62.5ms,filter = 011  see p.30 of data sheet
    //txBuffer[2] = 0x10;
    if (I2C_transfer(i2c, &i2cTransaction))
                    {
                        //light = (rxBuffer[0] << 8) | (rxBuffer[1]);
                        id = rxBuffer[0];
                        Display_printf(display, 0, 0, "Measure After Configuration : %d (C)",
                                        id);
                    }

// Configuration hum measure:
        i2cTransaction.writeCount = 2;
        txBuffer[0] = 0xF2;
        txBuffer[1] = 0x03; //00: skip, 01: oversamplingx1, 10: oversamplingx2
            //txBuffer[2] = 0x10;
            if (I2C_transfer(i2c, &i2cTransaction))
                            {
                                //light = (rxBuffer[0] << 8) | (rxBuffer[1]);
                id = rxBuffer[0];
                Display_printf(display, 0, 0, "Hum register After Configuration : %d (C)",
                                                id);
                            }

// Configuration MODE 00: sleep, 01,10: Force, 11: Normal
    i2cTransaction.writeCount = 2;
    txBuffer[0] = 0xF4;
    txBuffer[1] = 0x03; //t_sb =  10ms,filter = 2  see p.30 of datashhet
        //txBuffer[2] = 0x10;
        if (I2C_transfer(i2c, &i2cTransaction))
                        {
                            //light = (rxBuffer[0] << 8) | (rxBuffer[1]);
            id = rxBuffer[0];
            Display_printf(display, 0, 0, "Mode After Configuration : %d (C)",
                                            id);
                        }

 /* Read Calib coefficient of Humidity*/
    // READ dig_H1
    i2cTransaction.writeCount = 1;
    txBuffer[0] = 0xA1;
    if (I2C_transfer(i2c, &i2cTransaction))
    {

        dig_H1 = rxBuffer[0];
        Display_printf(display, 0, 0, "Coefficient dig_H1 : %u (C)",
                                                dig_H1);
     }
    //READ dig_H2 - digH6
    txBuffer[0] = 0xE1;
    i2cTransaction.readCount  = 7;
    if (I2C_transfer(i2c, &i2cTransaction))
       {

           dig_H2 = ((rxBuffer[1]<<8)|rxBuffer[0]);
           Display_printf(display, 0, 0, "Coefficient dig_H2 : %d (C)",
                          dig_H2);
           dig_H3 = rxBuffer[2];
                      Display_printf(display, 0, 0, "Coefficient dig_H3 : %u (C)",
                          dig_H3);
           dig_H4 = ((rxBuffer[3]<<4)|(0x0F&rxBuffer[4]));
           Display_printf(display, 0, 0, "Coefficient dig_H4 : %d (C)",
                          dig_H4);
           dig_H5 = ((rxBuffer[5]<<4)|((0xF0&rxBuffer[4])>>4));
           Display_printf(display, 0, 0, "Coefficient dig_H5 : %d (C)",
                          dig_H5);
           dig_H6 = rxBuffer[6];
           Display_printf(display, 0, 0, "Coefficient dig_H6 : %d (C)",
                          dig_H6);
        }
/* Take 20 samples and print them out onto the console */
     //i2cTransaction.writeBuf   = txBuffer;
     i2cTransaction.writeCount = 1;
     //i2cTransaction.readBuf    = rxBuffer;
     i2cTransaction.readCount  = 2;

    txBuffer[0] = 0xFD;

for (sample = 0; sample < 20; sample++) {
        if (I2C_transfer(i2c, &i2cTransaction)) {
            /*
             * Extract degrees C from the received data;
             * see TMP116/006 datasheet
             */
            //temperature = (rxBuffer[0] << 8) | (rxBuffer[1]);
            //temperature *= 0.0078125;

            /*
             * If the MSB is set '1', then we have a 2's complement
             * negative value which needs to be sign extended
             */
            //if (rxBuffer[0] & 0x80) {
            //    temperature |= 0xF000;

            //display ambient level light
            /*
            pow = (rxBuffer[0] >> 4) ;
            light = ((rxBuffer[0]&0x0F) << 8) | (rxBuffer[1]);
            while(pow!=0)
            {
                pow -=1;        // Multiply 2^n by left shifting to n times
                light <<=1;
            }
            light *=0.01;
            */
            adc_H = ((rxBuffer[0] << 8) | (rxBuffer[1]));
            hum = bme280_compensate_H_int32((int32_t)adc_H);
            hum >>=10;
            Display_printf(display, 0, 0, "Sample %u: %d (%c)",
                sample, hum,'%'); //temperature
        }
        else {
            Display_printf(display, 0, 0, "I2C Bus fault.");
        }

        /* Sleep for 1 second */
        sleep(1);
    }

    I2C_close(i2c);
    Display_printf(display, 0, 0, "I2C closed!");

    return (NULL);
}

When we read from I2C we got a raw value of humidity from two Register 0xFD (High Byte) 0xFE(Low Byte). The value will transfer to rxbuffer[0] and rxbuffer[1] respectively.
Next, we need to convert to real value using a compensation function as describe in P25-P26 of the datasheet

uint32_t bme280_compensate_H_int32(int32_t adc_H)
{
    int32_t v_x1_u32r;

    v_x1_u32r = t_fine - ((int32_t)76800);
    v_x1_u32r = (((((adc_H << 14) - (((int32_t)dig_H4) << 20) - (((int32_t)dig_H5) *
            v_x1_u32r))+ ((int32_t)16384)) >> 15) * (((((((v_x1_u32r*
            ((int32_t)dig_H6)) >> 10) * (((v_x1_u32r * ((int32_t)dig_H3)) >> 11) +
            ((int32_t)32768))) >> 10) + ((int32_t)2097152)) * ((int32_t)dig_H2) +
                    8192) >> 14));
    v_x1_u32r = (v_x1_u32r - (((((v_x1_u32r >> 15) * (v_x1_u32r >> 15)) >> 7) *
            ((int32_t)dig_H1)) >> 4 ));
    v_x1_u32r = (v_x1_u32r < 0 ? 0 : v_x1_u32r);
    v_x1_u32r = (v_x1_u32r > 419430400 ? 419430400 : v_x1_u32r);
    return (uint32_t)(v_x1_u32r>>12);
}
Notice: The values of calibration are fixed and we can store some elsewhere to reuse rather than access it each time we want to use BME280 to read humidity value.

dig_H1 = 0
dig_H2 = 379
dig_H3 = 0
dig_H4 = 281
dig_H5 = 50
dig_h6 = 30 

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