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184 O CHAPTER 3/COMBINATIONAL LOGIC DESIGN PROBLEMS The plus (+) indicates a more advanced problem and the asterisk () indicates th a solution is available on the text website. A majority function has an output value of 1 if there are more 1s than Os on its inputs. The output is 0 otherwise. Design a three-input majority function. 3-1. 3-2. Find a function to detect an error in the representation of a decimal digit in BCD. In other words, write an equation with value 1 when the inputs are any one of the six unused bit combinations in the BCD code, and value0 otherwise. 3-3. Design a Gray code-to-BCD code converter that gives output code 1111 for all invalid input combinations. Assume that the Gray code sequence for decimal numbers 0 through 9 is 0000, 0001, 0011, 0010, 0110, 0111, 0101, 0100, 1100, and 1101. All other input combinations should be considered to be invalid. 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 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 O if a winning pattern is not present. For of the nine squares, there are two signals, X, and O,.Two copies of the circuit are used, one for Xs and one for Os. Hint: Form a condensed truth table for W(XI,X2,... ,X9). (a) Design the X circuit for the following pattern of signals for the squares: O.) each ? 2? uch as nossible. using