# How doesn't JPEG huffman table contain 256 codes?

Here are the DHT entries I got from JPEG snoop:

  Destination ID = 1
Class = 1 (AC Table)
Codes of length 01 bits (000 total):
Codes of length 02 bits (002 total): 00 01
Codes of length 03 bits (001 total): 02
Codes of length 04 bits (002 total): 03 11
Codes of length 05 bits (004 total): 04 05 21 31
Codes of length 06 bits (004 total): 06 12 41 51
Codes of length 07 bits (003 total): 07 61 71
Codes of length 08 bits (004 total): 13 22 32 81
Codes of length 09 bits (007 total): 08 14 42 91 A1 B1 C1
Codes of length 10 bits (005 total): 09 23 33 52 F0
Codes of length 11 bits (004 total): 15 62 72 D1
Codes of length 12 bits (004 total): 0A 16 24 34
Codes of length 13 bits (000 total):
Codes of length 14 bits (001 total): E1
Codes of length 15 bits (002 total): 25 F1
Codes of length 16 bits (119 total): 17 18 19 1A 26 27 28 29 2A 35 36 37 38 39 3A 43
44 45 46 47 48 49 4A 53 54 55 56 57 58 59 5A 63
64 65 66 67 68 69 6A 73 74 75 76 77 78 79 7A 82
83 84 85 86 87 88 89 8A 92 93 94 95 96 97 98 99
9A A2 A3 A4 A5 A6 A7 A8 A9 AA B2 B3 B4 B5 B6 B7
B8 B9 BA C2 C3 C4 C5 C6 C7 C8 C9 CA D2 D3 D4 D5
D6 D7 D8 D9 DA E2 E3 E4 E5 E6 E7 E8 E9 EA F2 F3
F4 F5 F6 F7 F8 F9 FA
Total number of codes: 162


And

  Destination ID = 1
Class = 0 (DC / Lossless Table)
Codes of length 01 bits (000 total):
Codes of length 02 bits (003 total): 00 01 02
Codes of length 03 bits (001 total): 03
Codes of length 04 bits (001 total): 04
Codes of length 05 bits (001 total): 05
Codes of length 06 bits (001 total): 06
Codes of length 07 bits (001 total): 07
Codes of length 08 bits (001 total): 08
Codes of length 09 bits (001 total): 09
Codes of length 10 bits (001 total): 0A
Codes of length 11 bits (001 total): 0B
Codes of length 12 bits (000 total):
Codes of length 13 bits (000 total):
Codes of length 14 bits (000 total):
Codes of length 15 bits (000 total):
Codes of length 16 bits (000 total):
Total number of codes: 012


For AC table we are encoding the RRRRSSSS byte that contains zero run length and magnitude of nonzero AC coefficient that follows. This byte has 256 possible values. Then for DC we are encoding the SSSS nibble that can has 16 possible values.

Why then is it that in all the JPEG images I have seen, downloaded or created in MS Paint, the AC table has only 162 entries and DC has only 12? This means that for certain values of RRRRSSSS and SSSS, there is no way to compress them.

• Not all combinations are used. For example for AC coefficients the table has up to 10 runs of values of 1 to 16, plus two values for EOB and ZRL that becomes162 possibilities totally. – msm May 22 '17 at 5:25
• Jpeg images use all shades of colours that will generate all possible dct and diff values and all possible zero run length values. This gap makes no sense. – quantum231 May 22 '17 at 9:36