# Repeat Problem 3-4 for 4 x 4 tic-tac-toe, which is played on a four-by-four grid. Assume that

## Question:

Repeat Problem 3-4 for 4 x 4 tic-tac-toe, which is played on a four-by-four grid. Assume that the numbering pattern is left to right and top to bottom, as in Problem 3-4.

**Problem 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 turns. Each player chooses a square and places a mark in a square. (One player uses X and the other O.)

The irst 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, X_{i} and O_{i} . Two copies of the circuit are used, one for Xs and one for Os. Form a condensed truth table for W(X_{1}, X_{2}, . . . . X_{9}).

** (a) **Design the X circuit for the following pattern of signals for the squares:

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

## Step by Step Answer:

**Related Book For**

## Logic And Computer Design Fundamentals

**ISBN:** 9780133760637

5th Edition

**Authors:** M. Morris Mano, Charles Kime, Tom Martin