0x88

In the 0x88 board representation, the layout is spread out to cover an 8-by-16 board, equal to the size of two adjacent chessboards. Each square of the 8-by-16 matrix is assigned a number as can be seen in the board layout table. In this scheme each nibble represents a rank or a file, so that the 8-bit integer 0x42 represents the square at (4,2) in zero-based numbering, i.e. c5 in standard algebraic notation.[1]

Adding 16 to a number for a square results in the number for the square one row above, and subtracting 16 results in the number for the square one row below. To move from one column to another the number is increased or decreased by one.[2] In hexadecimal notation, legal chess positions (A1-H8) are always below 0x88. This layout simplifies many computations that chess programs need to perform by allowing bitwise operations instead of comparisons.[3]

Squares on a chess board with algebraic notation

The modern standard to identify the squares on a chessboard and moves in a game is algebraic notation, whereby each square of the board is identified by a unique coordinate pair — a letter between a and h for the horizontal coordinate, known as the file, and a number between 1 and 8 for the vertical coordinate, known as the rank.

In computer chess, file-rank coordinates are internally represented as integers ranging from 0 to 7, with file a mapping to 0 through to file h mapping to 7, while the rank coordinate is shifted down by one to the range 0 to 7.

An advantage of the 0x88 coding scheme is that values can be easily converted between 0x88 representation and file-rank coordinates using only bitwise operations, which are simple and efficient for computer processors to work with. To convert a zero-based file-rank coordinate to 0x88 value:

${\displaystyle {\text{square}}_{0{\rm {{x}88}}}=({\text{rank}}_{\text{0 to 7}}<<4)+{\text{file}}_{\text{0 to 7}}}$

Thus, a1 corresponds to ${\displaystyle 00000000_{2}}$, with all 8 of the bits set to ${\displaystyle 0}$, b2 corresponds to ${\displaystyle 00010001_{2}}$, and h8 corresponds to ${\displaystyle 01110111_{2}}$.[1]

To convert an 0x88 value to a file-rank coordinate pair:

${\displaystyle {\text{file}}_{\text{0 to 7}}={\text{square}}_{0{\rm {{x}88}}}\ \&\ 7}$

${\displaystyle {\text{rank}}_{\text{0 to 7}}=({\text{square}}_{0{\rm {{x}88}}}\ >>4)}$

Note: In the above formulas, << and >> represent left and right logical bit shift operations respectively while & represents bitwise and.

Though the 0x88 representation was initially popular, it has been mostly replaced by the system of bitboards.[7]

• Chess board representations by Robert Hyatt
• How Zarkov Plays Chess Archived 2020-08-19 at the Wayback Machine by John Stanback
• The 0x88 representation from Mediocre Chess Archived 2018-08-20 at the Wayback Machine by Jonatan Pettersson