Reading an absolute encoder with gray code output - arduino

Question

I have an absolute encoder(Hengstler AD36) that gives 12 bit position value with gray code. I am trying to convert that value to decimal, I mean in degrees 0 to 360.
I have the 12 bit value in gray code by using Arduino.I have read the Arduino port and converted it in Python, but I need to do it in Arduino. But, I couldn't convert it to any meaningful numbers in Arduino.
///Pin setup for the Sensor
const int CLOCK_PIN = 18;
const int DATA_PIN = 19;
const int DATA_PIN2 = 17;
///12-bit sensor
const int BIT_COUNT = 12;
void setup() {
//setup our pins
pinMode(DATA_PIN, INPUT);
pinMode(CLOCK_PIN, OUTPUT);
//give some default values
digitalWrite(CLOCK_PIN, HIGH);
Serial.begin(9600);
}
void loop() {
unsigned long reading1 = readPosition1();
Serial.print(reading1,BIN);
Serial.print(",");
delay(50);
}
//read the current angular position
int readPosition1() {
unsigned long sample1 = shiftIn(DATA_PIN, CLOCK_PIN, BIT_COUNT);
delayMicroseconds(25); // delay for clock
return sample1;
}
//read in a byte of data from the digital input of the board.
unsigned long shiftIn(const int data_pin, const int clock_pin, const int bit_count) {
unsigned long data = 0;
for (int i=0; i<bit_count; i++) {
data <<= 1;
digitalWrite(clock_pin, LOW);
delayMicroseconds(1);
digitalWrite(clock_pin, HIGH);
delayMicroseconds(1);
data |= digitalRead(data_pin);
}
return data;
}
How can I convert data to decimal (0 to 360 degrees)?
The main problem that I couldn't solve, I found some functions that convert gray code to binary, then it is easy to convert it to decimal. However, these functions take input as string or int, and I have no idea about converting data value to int.
Any help would be greatly appreciated.
Thanks.