Digital Logic Project 2: BCD Digit Design Design a logic circuit with 3 inputs (x, y, z) and an output, a 7-Segment Display. You are going to design circuit to convert 3 bits binary number to a decimal number in 7-Segment Display. The inputs and outputs are demonstrated in the table on the right. The 7-segment display is in the following Figure 1. x y z Output a b c d e f g 0 0 0 Submit K-map & simplified boolean expression for b, c, d, e, f, g, and the completed circuit to the dropbox. Remember to put the project number, your name, and identify the input with x, y, z, in the circuit file.

1 Procedure for designing a digital system

Instructions

Read Chapter 3.1-3.4, and summarize the 5 steps of the procedure for designing a digital system

Project 3: Tic-Tac-Toe

Digital Logic Pre-Exam

1. Fill in the blanks (30pts): (1).Convert 123.2510 (decimal) to binary ___________________________________. (2).Convert 59D.C16 (Hex) to binary _____________________________________ and octal _______________________. (3). Assume the word length is 6 bits, 2s complement of (810) is ____________________, 2s complement of (1110) is ____________________, the result of addition of these two number by using 2s complement is _(___)________________, and there _______(is/isnt) an overflow. (4). For F(A,B,C) = A + BC + BC, the minterm expansion of F is m(________________), the maxterm expansion of F is M(____________________), the minterm expansion of F is m(________________), the maxterm expansion of F is M(____________________).

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 Oi . 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

X7 X8 X9

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

Apply the 5 steps to design the circuit.

Your final resulted inputs will be line up like this:

X1 O1 X2 O2 X3 O3

X4 O4 X5 O5 X6 O6

X7 O7 X8 O8 X9 O9

And the outputs will be W1 representing X1-9, W2 representing O1-9. Whichever have a satisfied patten will turn to 1. Whichever turns to 1 first will be the winner.