Reading information from PAT section (MPEG-TS)

I'm writing a MPEG-TS file parser and I'm stuck on getting program_numbers and PIDs from the PAT section. I'm using a packet analyser to compare my results.

For example, here's a PAT packet

47 40 00 16 00 00 B0 31 00 14 D7 00 00 00 00 E0
10 00 01 E0 24 00 02 E0 25 00 03 E0 30 00 04 E0
31 00 1A E0 67 00 1C E0 6F 43 9D E3 F1 43 A3 E3
F7 43 AC E4 00 C3 69 A6 D8 FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
FF FF FF FF FF FF FF FF FF FF FF FF

First I began comparing the analyser's results to the bytes to see the connection. It paired bytes in the following way: [00 10][01 24][02 25][03 30] etc. I noticed a pattern (for i = 14; i < end; i+=4) but that quickly turned wrong because after the "0x6F" byte it started reading 16 bits, not 8, so the program_number was 0x439D.

I'm seriously confused and I hope that someone can explain to me how to parse the example PAT from above.

Each program_number is 16 bits and is followed by 16 bits consisting of 3 x '1' bits and a 13 bit program_map_pid (or network_pid ifprogram_number`=0)

Start at offset 13 in your dump and read pairs of 16-bit words, masking out the top 3 bits of the second word.

e.g.

offset   bytes          words        program_number pid
======   ===========    =========    ============== ======================
000D:    00 00 E0 10 => 0000 E010 => 0000           0010 (network_pid)
0011:    00 01 E0 24 => 0001 E024 => 0001           0024 (program_map_pid)
0015:    00 02 E0 25 => 0002 E025 => 0002           0025 (program_map_pid)
0019:    etc..
001D:    etc..
0021:    etc..
0025:    00 1C E0 6F => 001C E06F => 001C           006F (program_map_pid)
0029:    43 9D E3 F1 => 439D E3F1 => 439D           03F1 (program_map_pid)
002D:    etc..
etc..

In theory it is more complicated than this as there can be multiple program association sections in a PAT and the above will only help with the 1st section.

For more details see section 2.4.4.3 of ISO/IEC 13818-1, specifically table 2-25.