In numeric notation, each square is designated with a two-digit number via a coordinate system. The first digit describes the file and the second digit the rank. Files are numbered 1 to 8 from White's left to White's right, and ranks are numbered 1 to 8 from White's near side to White's far side. A move is defined by pairing two square designations together, one for the starting square and one for the ending square. For example, the move that would be written 1.e4 in algebraic notation would be written 1. 5254 in numeric notation: the pawn starts from square 52 (file 5, rank 2) and moves to square 54 (file 5, rank 4). Numeric notation does not explicitly mark the type of moving piece, captures, or checks; every move is written as four digits unless resulting in promotion.
For promotion, a fifth digit is added to the move's notation: 1 for queen, 2 for rook, 3 for bishop, and 4 for knight. For instance, a pawn on f7 moving to f8 and promoting to a rook would be written as 67682. A variant four-digit notation where the ending rank is omitted (because it is always 8 for White and 1 for Black) also exists (e.g. 6762); however, this is considered confusing and contradicts the standard.
Castling is written using the king's start position and end position. Castling kingside is written as 5171 for White and 5878 for Black, and castling queenside is written as 5131 for White and 5838 for Black. The rook's start and end positions are implied.
German professor J. W. D. Wildt of Göttingen devised numeric notation circa 1803. Johann Koch used the system 25 years later; the system is sometimes named after him. Ivan Savenkov supported its use in 1877, and it bears his name in Russia.
(Just & Burg 2003:221–22) - Just, Tim; Burg, Daniel B. (2003), U.S. Chess Federation's Official Rules of Chess (fifth ed.), McKay, ISBN 0-8129-3559-4 ↩