3-4. A simple well-known game, tic-tac-toe, is played on a three-by-three grid of squares by two...

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3-4. A simple well-known game, tic-tac-toe, is played on a three-by-three grid of squares by two players. The players alternate tums. Each player chooses a square and places a mark in a square. (One player uses X and the other O.) The first player with three marks in a row, in a column, or on a diagonal wins the game. A logic circuit is to be designed for an electronic tic-tac-toe that indicates the presence of a winning pattern. The circuit output Wis a 1 if a winning pattern is present and a 0 if a winning pattern is not present. For each of the nine squares, there are two signals, X, and O₁. Two copies of the circuit are used, one for Xs and one for Os. Hint: Form a condensed truth table for W(X₁, X₂,..., X9). (a) Design the X circuit for the following pattern of signals for the squares: X₁ X₂ X3 X4 X5 X6 X7X8 X9 (b) Minimize the Woutput for the circuit as much as possible, using Boolean algebra. 3-4. A simple well-known game, tic-tac-toe, is played on a three-by-three grid of squares by two players. The players alternate tums. Each player chooses a square and places a mark in a square. (One player uses X and the other O.) The first player with three marks in a row, in a column, or on a diagonal wins the game. A logic circuit is to be designed for an electronic tic-tac-toe that indicates the presence of a winning pattern. The circuit output Wis a 1 if a winning pattern is present and a 0 if a winning pattern is not present. For each of the nine squares, there are two signals, X, and O₁. Two copies of the circuit are used, one for Xs and one for Os. Hint: Form a condensed truth table for W(X₁, X₂,..., X9). (a) Design the X circuit for the following pattern of signals for the squares: X₁ X₂ X3 X4 X5 X6 X7X8 X9 (b) Minimize the Woutput for the circuit as much as possible, using Boolean algebra.