Binary Number Scrabble - The Game

Step 2 The Rules

• Except as noted, game play is similar to Scrabble (and Number Scrabble)
• On each turn, players must make or add to a valid and correct equation.
• Players keep 9 tiles in their hand at all times, not 7 as in normal Scrabble
• Players form valid equations (using binary number notation) rather than words.
  • example: '1+1=10'
• Besides the PLUS, MINUS, MULTIPLY and DIVIDE operations, you also have available the 3 basic Bitwise Logical Operations AND, OR and NOT.
  
  • example: '100 OR 1 = 101'
• You can add to an existing equation on one side or both sides in a single turn.
  • example: you can add to both ends of '1+1=10' in a single turn to make '11+1=100'
• You may only use one new '=' sign per turn
• Order of operation:  The game will function correctly as long as you agree beforehand on the order of operation.  You can play with either "standard math" (ie, "x" preceeds "+" unrelated to the written order), or  "strict left-to-right evaluation".
  • NOT (inverse) operator applies only to the immediately following number
  • There is no implied multiplication
• Equations can have multiple equal parts.
  • example: '10x10=100=11+1'
• Redundant equations are valid
  • example: '1-1+1-1=0=0+0'
• Negative numbers are prohibited unless you can agree upon your means of applying AND, OR and NOT to them. :)
• You may not use leading '+' signs in front of a number
• When using AND and OR on two numbers of unequal length, leading zero's are assumed on the shorter number.  Leading zeros are not assumed for NOT.
  
  • example:  '101 AND 1 = 1'
• You may not use leading zeros in front of a number except when strictly required with a NOT to form a valid logic operation, in which case they must be used.
  
  • example: '110 = NOT 001'.
• You may not string together arbitrary symbols
  • example: '1+xx1==10' is NOT valid.
• In normal scrabble, you can place one word alongside another if they create a valid cross-word.  Here, a 2-character sequence can never be an equation so this generally is not possible.  As an optional rule, you may choose to allow placing alongside when only numbers are formed as the cross-words, but you still need to connect to an existing equation some other way.
• As an optional rule, you may choose to disallow the following "Identity" equation fragments:
  
  • "x1"   example:  you could not turn '1+1=10' to '1+1=10x1'
  • "+0" and "-0".   example:  you could not turn '3+4=7' to '3+4=7+0'
  • optionally "AND 1" and "OR 0" as well.
  • I recommend allowing these when playing in a learning scenario, but disallowing them with experienced players as you get into tedious '1+1=10+0+0+0x1x1' situations.
• Feel free to add XOR for Xtra fun!