/*! * \file galileo_cnav_message.cc * \brief Implementation of a Galileo CNAV Data message as described in * Galileo High Accuracy Service E6-B Signal-In-Space Message Specification v1.2 * (April 2020) * \author Carles Fernandez-Prades, 2020 cfernandez(at)cttc.es * * ----------------------------------------------------------------------------- * * Copyright (C) 2010-2020 (see AUTHORS file for a list of contributors) * * GNSS-SDR is a software defined Global Navigation * Satellite Systems receiver * * This file is part of GNSS-SDR. * * SPDX-License-Identifier: GPL-3.0-or-later * * ----------------------------------------------------------------------------- */ #include "galileo_cnav_message.h" #include // for boost::crc_basic, boost::crc_optimal #include // for boost::dynamic_bitset #include // for reverse, find #include // for accumulate using CRC_Galileo_CNAV_type = boost::crc_optimal<24, 0x1864CFBU, 0x0, 0x0, false, false>; bool Galileo_Cnav_Message::CRC_test(std::bitset bits, uint32_t checksum) const { CRC_Galileo_CNAV_type CRC_Galileo; // Galileo CNAV frame for CRC is not an integer multiple of bytes // it needs to be filled with zeroes at the start of the frame. // This operation is done in the transformation from bits to bytes // using boost::dynamic_bitset. boost::dynamic_bitset frame_bits(std::string(bits.to_string())); std::vector bytes; boost::to_block_range(frame_bits, std::back_inserter(bytes)); std::reverse(bytes.begin(), bytes.end()); CRC_Galileo.process_bytes(bytes.data(), GALILEO_CNAV_BYTES_FOR_CRC); const uint32_t crc_computed = CRC_Galileo.checksum(); if (checksum == crc_computed) { return true; } return false; } void Galileo_Cnav_Message::read_HAS_page(const std::string& page_string) { const std::string has_page_bits = page_string.substr(0, GALILEO_CNAV_BITS_FOR_CRC); const std::string CRC_data = page_string.substr(GALILEO_CNAV_BITS_FOR_CRC, GALILEO_CNAV_CRC_LENGTH); const std::bitset Word_for_CRC_bits(has_page_bits); const std::bitset checksum(CRC_data); if (CRC_test(Word_for_CRC_bits, checksum.to_ulong()) == true) { d_flag_CRC_test = true; // CRC correct: Read HAS page header read_HAS_page_header(page_string.substr(GALILEO_CNAV_PAGE_RESERVED_BITS, GALILEO_CNAV_PAGE_HEADER_BITS)); bool use_has = false; d_test_mode = false; switch (d_has_page_status) { case 0: // HAS is in Test Mode use_has = true; d_test_mode = true; break; case 1: // HAS is in Operational Mode use_has = true; break; default: break; } if (use_has) { process_HAS_page(page_string.substr(GALILEO_CNAV_PAGE_RESERVED_BITS + GALILEO_CNAV_PAGE_HEADER_BITS, GALILEO_CNAV_MESSAGE_BITS_PER_PAGE)); } } else { d_flag_CRC_test = false; } } void Galileo_Cnav_Message::read_HAS_page_header(const std::string& page_string) { // check if dummy if (page_string == "101011110011101111000011") // Equivalent to AF3BC3 { d_page_dummy = true; } else { d_page_dummy = false; } if (!d_page_dummy) { const std::bitset has_page_header(page_string); d_has_page_status = read_has_page_header_parameter(has_page_header, GALILEO_HAS_STATUS); d_received_message_type = read_has_page_header_parameter(has_page_header, GALILEO_HAS_MESSAGE_TYPE); d_received_message_id = read_has_page_header_parameter(has_page_header, GALILEO_HAS_MESSAGE_ID); d_received_message_size = read_has_page_header_parameter(has_page_header, GALILEO_HAS_MESSAGE_SIZE); d_received_message_page_id = read_has_page_header_parameter(has_page_header, GALILEO_HAS_MESSAGE_PAGE_ID); } } void Galileo_Cnav_Message::process_HAS_page(const std::string& page_string) { if (d_current_message_id == d_received_message_id) { // if receiver pid was not there, store it. if (std::find(d_list_pid.begin(), d_list_pid.end(), d_received_message_page_id) == d_list_pid.end()) { if (d_received_message_type == 1) // contains satellite corrections { d_received_encoded_messages++; d_list_pid.push_back(d_received_message_page_id); // Store encoded page d_encoded_message_type_1 += std::string(page_string); } } } else { // Start new message d_current_message_id = d_received_message_id; d_received_encoded_messages = 0; d_new_message = false; d_current_message_size = d_received_message_size; // erase stored pages and start storing again d_encoded_message_type_1.clear(); d_list_pid.clear(); if (d_received_message_type == 1) { d_encoded_message_type_1.reserve(GALILEO_CNAV_MAX_NUMBER_ENCODED_BLOCKS * GALILEO_CNAV_MESSAGE_BITS_PER_PAGE); d_received_encoded_messages++; d_list_pid.push_back(d_received_message_page_id); d_encoded_message_type_1 += std::string(page_string); } } if (d_received_encoded_messages == d_current_message_size) { // we have a full encoded message stored in d_encoded_message_type_1 d_received_encoded_messages = 0; d_current_message_id = 0; d_new_message = true; decode_message_type1(); } } void Galileo_Cnav_Message::decode_message_type1() { // TODO: Reed-Solomon decoding of d_encoded_message_type_1 // TODO: reordering // decoded_message_type1 = ... // read_HAS_message_type1(decoded_message_type1); } void Galileo_Cnav_Message::read_HAS_message_type1(const std::string& message_string) { d_HAS_data = Galileo_HAS_data(); read_MT1_header(message_string); read_MT1_body(message_string); } void Galileo_Cnav_Message::read_MT1_header(const std::string& message_string) { const std::bitset has_mt1_header(message_string); d_HAS_data.header.toh = read_has_message_header_parameter_uint16(has_mt1_header, GALILEO_MT1_HEADER_TOH); d_HAS_data.header.mask_id = read_has_message_header_parameter_uint8(has_mt1_header, GALILEO_MT1_HEADER_MASK_ID); d_HAS_data.header.iod_id = read_has_message_header_parameter_uint8(has_mt1_header, GALILEO_MT1_HEADER_IOD_ID); d_HAS_data.header.mask_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_MASK_FLAG); d_HAS_data.header.orbit_correction_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_ORBIT_CORRECTION_FLAG); d_HAS_data.header.clock_fullset_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_CLOCK_FULLSET_FLAG); d_HAS_data.header.clock_subset_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_CLOCK_SUBSET_FLAG); d_HAS_data.header.code_bias_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_CODE_BIAS_FLAG); d_HAS_data.header.phase_bias_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_PHASE_BIAS_FLAG); d_HAS_data.header.ura_flag = read_has_message_header_parameter_bool(has_mt1_header, GALILEO_MT1_HEADER_URA_FLAG); } void Galileo_Cnav_Message::read_MT1_body(const std::string& message_string) { auto message = std::string(message_string.begin() + GALILEO_CNAV_MT1_HEADER_BITS, message_string.end()); // Remove header int Nsat = 0; if (d_HAS_data.header.mask_flag) { // read mask d_HAS_data.Nsys = read_has_message_body_uint8(message.substr(0, HAS_MSG_NSYS_LENGTH)); message = std::string(message.begin() + HAS_MSG_NSYS_LENGTH, message.end()); d_HAS_data.gnss_id_mask.reserve(d_HAS_data.Nsys); d_HAS_data.cell_mask.reserve(d_HAS_data.Nsys); d_HAS_data.cell_mask_availability_flag.reserve(d_HAS_data.Nsys); d_HAS_data.nav_message.reserve(d_HAS_data.Nsys); for (uint8_t i = 0; i < d_HAS_data.Nsys; i++) { d_HAS_data.gnss_id_mask[i] = read_has_message_body_uint8(message.substr(0, HAS_MSG_ID_MASK_LENGTH)); message = std::string(message.begin() + HAS_MSG_ID_MASK_LENGTH, message.end()); std::string msg = message.substr(0, HAS_MSG_SATELLITE_MASK_LENGTH); d_HAS_data.satellite_mask[i] = read_has_message_body_uint64(msg); int ones_in_satellite_mask = 0; for (size_t i = 0; i < msg.length(); i++) { if (msg[i] == '1') { ones_in_satellite_mask++; } } Nsat += ones_in_satellite_mask; message = std::string(message.begin() + HAS_MSG_SATELLITE_MASK_LENGTH, message.end()); msg = message.substr(0, HAS_MSG_SIGNAL_MASK_LENGTH); d_HAS_data.signal_mask[i] = read_has_message_body_uint16(msg); int ones_in_signal_mask = 0; for (size_t i = 0; i < msg.length(); i++) { if (msg[i] == '1') { ones_in_signal_mask++; } } message = std::string(message.begin() + HAS_MSG_SIGNAL_MASK_LENGTH, message.end()); if (message.substr(0, 1) == "1") { d_HAS_data.cell_mask_availability_flag[i] = true; } else { d_HAS_data.cell_mask_availability_flag[i] = false; } message = std::string(message.begin() + 1, message.end()); int size_cell = ones_in_satellite_mask * ones_in_signal_mask; d_HAS_data.cell_mask[i].reserve(ones_in_satellite_mask); for (int s = 0; s < ones_in_satellite_mask; s++) { d_HAS_data.cell_mask[i][s].reserve(ones_in_signal_mask); for (int sig = 0; sig < ones_in_signal_mask; sig++) { d_HAS_data.cell_mask[i][s][sig] = (message[sig] == '1' ? true : false); } } message = std::string(message.begin() + size_cell, message.end()); d_HAS_data.nav_message[i] = read_has_message_body_uint8(message.substr(0, HAS_MSG_NAV_MESSAGE_LENGTH)); message = std::string(message.begin() + HAS_MSG_NAV_MESSAGE_LENGTH, message.end()); } } if (d_HAS_data.header.orbit_correction_flag) { // read orbit corrections d_HAS_data.validity_interval_index_orbit_corrections = read_has_message_body_uint8(message.substr(0, HAS_MSG_VALIDITY_INDEX_LENGTH)); message = std::string(message.begin() + HAS_MSG_VALIDITY_INDEX_LENGTH, message.end()); d_HAS_data.gnss_iod.reserve(Nsat); d_HAS_data.delta_radial.reserve(Nsat); d_HAS_data.delta_along_track.reserve(Nsat); d_HAS_data.delta_cross_track.reserve(Nsat); for (int i = 0; i < Nsat; i++) { if (d_HAS_data.gnss_id_mask[i] == HAS_MSG_GPS_SYSTEM) { d_HAS_data.gnss_iod[i] = read_has_message_body_uint16(message.substr(0, HAS_MSG_IOD_GPS_LENGTH)); message = std::string(message.begin() + HAS_MSG_IOD_GPS_LENGTH, message.end()); } if (d_HAS_data.gnss_id_mask[i] == HAS_MSG_GALILEO_SYSTEM) { d_HAS_data.gnss_iod[i] = read_has_message_body_uint16(message.substr(0, HAS_MSG_IOD_GAL_LENGTH)); message = std::string(message.begin() + HAS_MSG_IOD_GAL_LENGTH, message.end()); } d_HAS_data.delta_radial[i] = read_has_message_body_int16(message.substr(0, HAS_MSG_DELTA_RADIAL_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_RADIAL_LENGTH, message.end()); d_HAS_data.delta_along_track[i] = read_has_message_body_int16(message.substr(0, HAS_MSG_DELTA_ALONG_TRACK_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_ALONG_TRACK_LENGTH, message.end()); d_HAS_data.delta_cross_track[i] = read_has_message_body_int16(message.substr(0, HAS_MSG_DELTA_CROSS_TRACK_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_CROSS_TRACK_LENGTH, message.end()); } } if (d_HAS_data.header.clock_fullset_flag) { // read clock full-set corrections d_HAS_data.validity_interval_index_clock_fullset_corrections = read_has_message_body_uint8(message.substr(0, HAS_MSG_VALIDITY_INDEX_LENGTH)); message = std::string(message.begin() + HAS_MSG_VALIDITY_INDEX_LENGTH, message.end()); d_HAS_data.delta_clock_c0_multiplier.reserve(d_HAS_data.Nsys); for (uint8_t i = 0; i < d_HAS_data.Nsys; i++) { if (d_HAS_data.gnss_id_mask[i] != HAS_MSG_GALILEO_SYSTEM) { d_HAS_data.delta_clock_c0_multiplier[i] = read_has_message_body_uint8(message.substr(0, HAS_MSG_DELTA_CLOCK_C0_MULTIPLIER_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_CLOCK_C0_MULTIPLIER_LENGTH, message.end()); } } d_HAS_data.iod_change_flag.reserve(Nsat); d_HAS_data.delta_clock_c0.reserve(Nsat); for (int i = 0; i < Nsat; i++) { d_HAS_data.iod_change_flag[i] = (message[0] == '1' ? true : false); message = std::string(message.begin() + 1, message.end()); d_HAS_data.delta_clock_c0[i] = read_has_message_body_int16(message.substr(0, HAS_MSG_DELTA_CLOCK_C0_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_CLOCK_C0_LENGTH, message.end()); } } if (d_HAS_data.header.clock_subset_flag) { // read clock subset corrections d_HAS_data.validity_interval_index_clock_subset_corrections = read_has_message_body_uint8(message.substr(0, HAS_MSG_VALIDITY_INDEX_LENGTH)); message = std::string(message.begin() + HAS_MSG_VALIDITY_INDEX_LENGTH, message.end()); d_HAS_data.Nsysprime = read_has_message_body_uint8(message.substr(0, HAS_MSG_NSYSPRIME_LENGTH)); message = std::string(message.begin() + HAS_MSG_NSYSPRIME_LENGTH, message.end()); d_HAS_data.gnss_id_clock_subset.reserve(d_HAS_data.Nsysprime); d_HAS_data.delta_clock_c0_multiplier_clock_subset.reserve(d_HAS_data.Nsysprime); d_HAS_data.satellite_submask.reserve(d_HAS_data.Nsysprime); d_HAS_data.iod_change_flag_clock_subset.reserve(d_HAS_data.Nsysprime); d_HAS_data.delta_clock_c0_clock_subset.reserve(d_HAS_data.Nsysprime); for (uint8_t i = 0; i < d_HAS_data.Nsysprime; i++) { d_HAS_data.gnss_id_clock_subset[i] = read_has_message_body_uint8(message.substr(0, HAS_MSG_ID_CLOCK_SUBSET_LENGTH)); message = std::string(message.begin() + HAS_MSG_ID_CLOCK_SUBSET_LENGTH, message.end()); if (d_HAS_data.gnss_id_clock_subset[i] != HAS_MSG_GALILEO_SYSTEM) { d_HAS_data.delta_clock_c0_multiplier_clock_subset[i] = read_has_message_body_uint8(message.substr(0, HAS_MSG_DELTA_CLOCK_MULTIPLIER_SUBSET_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_CLOCK_MULTIPLIER_SUBSET_LENGTH, message.end()); } int number_sats_this_gnss_id = 0; for (uint8_t j = 0; j < d_HAS_data.Nsys; j++) { if (d_HAS_data.gnss_id_mask[j] == d_HAS_data.gnss_id_clock_subset[i]) { uint64_t n = d_HAS_data.satellite_mask[j]; while (n) { number_sats_this_gnss_id += n & 1; n >>= 1; } break; } } d_HAS_data.satellite_submask[i].reserve(number_sats_this_gnss_id); for (int j = 0; j < number_sats_this_gnss_id; j++) { d_HAS_data.satellite_submask[i][j] = read_has_message_body_uint64(message.substr(0, 1)); message = std::string(message.begin() + 1, message.end()); } d_HAS_data.iod_change_flag_clock_subset[i] = (message[0] == '1' ? true : false); message = std::string(message.begin() + 1, message.end()); d_HAS_data.delta_clock_c0_clock_subset[i] = read_has_message_body_int16(message.substr(0, HAS_MSG_DELTA_CLOCK_C0_SUBSET_LENGTH)); message = std::string(message.begin() + HAS_MSG_DELTA_CLOCK_C0_SUBSET_LENGTH, message.end()); } } if (d_HAS_data.header.code_bias_flag) { // read code bias d_HAS_data.validity_interval_index_code_bias_corrections = read_has_message_body_uint8(message.substr(0, HAS_MSG_VALIDITY_INDEX_LENGTH)); message = std::string(message.begin() + HAS_MSG_VALIDITY_INDEX_LENGTH, message.end()); std::vector number_sats(d_HAS_data.Nsys, 0); std::vector number_codes(d_HAS_data.Nsys, 0); for (int sys = 0; sys < d_HAS_data.Nsys; sys++) { int number_sats_this_gnss_id = 0; int number_signals_this_gnss_id = 0; if (d_HAS_data.cell_mask_availability_flag[sys] == true) { uint64_t n = d_HAS_data.satellite_mask[sys]; while (n) { number_sats_this_gnss_id += n & 1; n >>= 1; } uint64_t m = d_HAS_data.signal_mask[sys]; while (m) { number_signals_this_gnss_id += m & 1; m >>= 1; } } else { number_sats_this_gnss_id = HAS_MSG_MAX_SATS; number_signals_this_gnss_id = HAS_MSG_MAX_SIGNALS; } number_sats[sys] = number_sats_this_gnss_id; number_codes[sys] = number_signals_this_gnss_id; } int Nsat_b = std::accumulate(number_sats.begin(), number_sats.end(), 0); d_HAS_data.code_bias.reserve(Nsat_b); int sat = 0; for (int sys = 0; sys < d_HAS_data.Nsys; sys++) { d_HAS_data.code_bias[sat].reserve(number_codes[sys]); for (int c = 0; c < number_codes[sys]; c++) { d_HAS_data.code_bias[sat][c] = read_has_message_body_int16(message.substr(0, HAS_MSG_CODE_BIAS_LENGTH)); message = std::string(message.begin() + HAS_MSG_CODE_BIAS_LENGTH, message.end()); sat += 1; } } } if (d_HAS_data.header.phase_bias_flag) { // read phase bias d_HAS_data.validity_interval_index_phase_bias_corrections = read_has_message_body_uint8(message.substr(0, HAS_MSG_VALIDITY_INDEX_LENGTH)); message = std::string(message.begin() + HAS_MSG_VALIDITY_INDEX_LENGTH, message.end()); std::vector number_sats(d_HAS_data.Nsys, 0); std::vector number_phases(d_HAS_data.Nsys, 0); for (int sys = 0; sys < d_HAS_data.Nsys; sys++) { int number_sats_this_gnss_id = 0; int number_signals_this_gnss_id = 0; if (d_HAS_data.cell_mask_availability_flag[sys] == true) { uint64_t n = d_HAS_data.satellite_mask[sys]; while (n) { number_sats_this_gnss_id += n & 1; n >>= 1; } uint64_t m = d_HAS_data.signal_mask[sys]; while (m) { number_signals_this_gnss_id += m & 1; m >>= 1; } } else { number_sats_this_gnss_id = HAS_MSG_MAX_SATS; number_signals_this_gnss_id = HAS_MSG_MAX_SIGNALS; } number_sats[sys] = number_sats_this_gnss_id; number_phases[sys] = number_signals_this_gnss_id; } int Nsat_p = std::accumulate(number_sats.begin(), number_sats.end(), 0); d_HAS_data.phase_bias.reserve(Nsat_p); d_HAS_data.phase_discontinuity_indicator.reserve(Nsat_p); int sat = 0; for (int sys = 0; sys < d_HAS_data.Nsys; sys++) { d_HAS_data.phase_bias[sat].reserve(number_phases[sys]); d_HAS_data.phase_discontinuity_indicator[sat].reserve(number_phases[sys]); for (int p = 0; p < number_phases[sys]; p++) { d_HAS_data.phase_bias[sat][p] = read_has_message_body_int16(message.substr(0, HAS_MSG_PHASE_BIAS_LENGTH)); message = std::string(message.begin() + HAS_MSG_PHASE_BIAS_LENGTH, message.end()); d_HAS_data.phase_discontinuity_indicator[sat][p] = read_has_message_body_uint8(message.substr(0, HAS_MSG_PHASE_DISCONTINUITY_INDICATOR_LENGTH)); message = std::string(message.begin() + HAS_MSG_PHASE_DISCONTINUITY_INDICATOR_LENGTH, message.end()); sat += 1; } } } if (d_HAS_data.header.ura_flag) { // read URA d_HAS_data.validity_interval_index_ura_corrections = read_has_message_body_uint8(message.substr(0, HAS_MSG_VALIDITY_INDEX_LENGTH)); message = std::string(message.begin() + HAS_MSG_VALIDITY_INDEX_LENGTH, message.end()); d_HAS_data.ura.reserve(Nsat); for (int i = 0; i < Nsat; i++) { d_HAS_data.ura[i] = read_has_message_body_uint8(message.substr(0, HAS_MSG_URA_LENGTH)); message = std::string(message.begin() + HAS_MSG_URA_LENGTH, message.end()); } } } uint8_t Galileo_Cnav_Message::read_has_page_header_parameter(std::bitset bits, const std::pair& parameter) const { uint8_t value = 0U; for (int j = 0; j < parameter.second; j++) { value <<= 1U; // shift left if (static_cast(bits[GALILEO_CNAV_PAGE_HEADER_BITS - parameter.first - j]) == 1) { value += 1; // insert the bit } } return value; } uint8_t Galileo_Cnav_Message::read_has_message_header_parameter_uint8(std::bitset bits, const std::pair& parameter) const { uint8_t value = 0U; for (int j = 0; j < parameter.second; j++) { value <<= 1U; // shift left if (static_cast(bits[GALILEO_CNAV_MT1_HEADER_BITS - parameter.first - j]) == 1) { value += 1; // insert the bit } } return value; } uint16_t Galileo_Cnav_Message::read_has_message_header_parameter_uint16(std::bitset bits, const std::pair& parameter) const { uint16_t value = 0U; for (int j = 0; j < parameter.second; j++) { value <<= 1U; // shift left if (static_cast(bits[GALILEO_CNAV_MT1_HEADER_BITS - parameter.first - j]) == 1) { value += 1; // insert the bit } } return value; } bool Galileo_Cnav_Message::read_has_message_header_parameter_bool(std::bitset bits, const std::pair& parameter) const { bool value = false; if (static_cast(bits[GALILEO_CNAV_MT1_HEADER_BITS - parameter.first]) == 1) { value = true; } return value; } uint8_t Galileo_Cnav_Message::read_has_message_body_uint8(const std::string& bits) const { uint8_t value = 0U; size_t len = bits.length(); for (size_t j = 0; j < len; j++) { value <<= 1U; // shift left if (static_cast(bits[len - 1 - j]) == 1) { value += 1; // insert the bit } } return value; } uint16_t Galileo_Cnav_Message::read_has_message_body_uint16(const std::string& bits) const { uint16_t value = 0U; size_t len = bits.length(); for (size_t j = 0; j < len; j++) { value <<= 1U; // shift left if (static_cast(bits[len - 1 - j]) == 1) { value += 1; // insert the bit } } return value; } uint64_t Galileo_Cnav_Message::read_has_message_body_uint64(const std::string& bits) const { uint64_t value = 0U; size_t len = bits.length(); for (size_t j = 0; j < len; j++) { value <<= 1U; // shift left if (static_cast(bits[len - 1 - j]) == 1) { value += 1; // insert the bit } } return value; } int16_t Galileo_Cnav_Message::read_has_message_body_int16(const std::string& bits) const { int16_t value = 0; size_t len = bits.length(); // read the MSB and perform the sign extension if (static_cast(bits[len - 1]) == 1) { value ^= 0xFFFF; // 16 bits variable } else { value &= 0; } for (size_t j = 0; j < len; j++) { value *= 2; // shift left the signed integer value &= 0xFFFE; // reset the corresponding bit (for the 16 bits variable) if (static_cast(bits[len - 1 - j]) == 1) { value += 1; // insert the bit } } return value; }