A simple well-known game, tic-tac-toe, is played on a three-by-three grid of squ

Question

A simple well-known game, tic-tac-toe, is played on a three-by-three grid of
squares by two players. The players alternate turns. 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 W is 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, Xi and Oj. Two copies of the
circuit are used, one for Xs and one for Os.

(a) Design the X circuit for the following pattern of signals for the squares:
X1 X2 X3
X4 X5 X6
X7 X8 X9

(b) Minimize the W output for the X circuit as much as possible, using Boolean
algebra.

Explanation / Answer

A simple well-known game, tic-tac-toe, is played on a three-by-three grid of squ

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