byte previousPinStates = 0;

void print4Bits(byte b) {
  for (int i = 3; i >= 0; --i) Serial.print(bitRead(b, i));
  Serial.println();
}

void handleNibble(byte b) {
  switch (b) {
    case 0b0000:
      // Do something for 0b0000
      Serial.println("Case 0");
      break;

    case 0b0001:
      // Do something for 0b0001
      Serial.println("Case 1");
      break;

    case 0b0010:
      // Do something for 0b0010
      Serial.println("Case 2");
      break;

    case 0b0011:
      // Do something for 0b0011
      Serial.println("Case 3");
      break;

    case 0b0100:
      // Do something for 0b0100
      Serial.println("Case 4");
      break;

    case 0b0101:
      // Do something for 0b0101
      Serial.println("Case 5");
      break;

    case 0b0110:
      // Do something for 0b0110
      Serial.println("Case 6");
      break;

    case 0b0111:
      // Do something for 0b0111
      Serial.println("Case 7");
      break;

    case 0b1000:
      // Do something for 0b1000
      Serial.println("Case 8");
      break;

    case 0b1001:
      // Do something for 0b1001
      Serial.println("Case 9");
      break;

    case 0b1010:
      // Do something for 0b1010
      Serial.println("Case A");
      break;

    case 0b1011:
      // Do something for 0b1011
      Serial.println("Case B");
      break;

    case 0b1100:
      // Do something for 0b1100
      Serial.println("Case C");
      break;

    case 0b1101:
      // Do something for 0b1101
      Serial.println("Case D");
      break;

    case 0b1110:
      // Do something for 0b1110
      Serial.println("Case E");
      break;

    case 0b1111:
      // Do something for 0b1111
      Serial.println("Case F");
      break;

    default:
      // Handle unexpected values
      Serial.println("Unknown case");
      break;
  }
}

void setup() {
  Serial.begin(115200);
  DDRD  &= B10000111;  // pins D3, D4, D5, D6 as INPUT
  PORTD |= B01111000;  // pins D3, D4, D5, D6 HIGH <==> PULLUP
  previousPinStates = ~(PIND >> 3)& 0b1111;
  Serial.print("start state : "); print4Bits(previousPinStates);
}

void loop() {
  byte nibble = ~(PIND >> 3) & 0b1111;
  if (nibble != previousPinStates) {
    Serial.print("new state : "); print4Bits(nibble);
    previousPinStates = nibble;
    handleNibble(nibble);
    delay(20); // poor's man anti bounce
  }
}