Given
Needle  : 1010 0011 1101 1100
Haystack: 0001 0010 1101 1100 1010 1101 0001 1110 1110 0111

1) Make three more copies of given, each bit-shifted
Needle A: 1010 0011 1101 1100
Needle B: x101 0001 1110 1110 0xxx
Needle C: xx10 1000 1111 0111 00xx
Needle D: xxx1 0100 0111 1011 100x
Column     D    C    B    A

2) Build the BM skip table based on the last complete byte
      D    C    B    A
0000 ---- ---- ---- 4444
0001 ---W -M-- ---- ----
0010 --X- ---- ---- ----
0011 ---W M--- ---- ----
0100 ---- ---M ---- ----
0101 -Y-W ---- ---- ----
0110 --X- ---- ---- ----
0111 ---W ---- ---M --M-
1000 ---- --M- ---- ----
1001 ---W ---- ---- ----
1010 Z-X- ---- ---- ----
1011 ---W ---- ---- ---M
1100 ---- ---- ---- M---
1101 -Y-W ---- M--- ----
1110 --X- ---- -M-- -M--
1111 ---W ---- --M- ----

 - : an entry I didn't try to determine yet
 M : Matched byte position, match previous needle 
     char to previous table column.
 Z : Perfect match found
 Y : Perfect match if byte after position A matches
     remnant B
 X : Perfect match if byte after position A matches
     remnant C
 W : Perfect match if byte after position A matches
     remnant D
1-4: mismatch, skip 1..4 bytes and restart scan
     at position A