Chapter 15 Homework logic design

Chapter 15 Homework 1. Explain ways in which a SM chart can simplify the design process. Use bullet format. -Visualizing the System: Provides a clear picture of the entire system structure. -Clarifying Relationships: Shows how different parts of the system relate to each other. -Reducing Complexity: Breaks down complex systems into manageable components. -Aiding Communication: Facilitates understanding and communication among team members. -Supporting Decision-Making: Helps in making informed design decisions by presenting a comprehensive view of the system. 2. Turn this truth table into a SM chart in Figure HW15.1. The problem is a Moore sequence detector that is looking for the sequence “1100” or “0100”. Overlapping targets are allowed. Since either a 0 or a 1 can be the first item of a target, this means we will never go back to S 0 once we start the process. (Note this is the answer to problem #2 for chapter 13 homework.) Present State Next State Output X = 0 X = 1 S 0 S 1 S 1 0 S 1 S 1 S 2 0 S 2 S 3 S 2 0 S 3 S 4 S 2 0 S 4 S 1 S 1 1 Figure HW15.1 State table to change to SM chart a) Draw the SM chart b) Draw the state graph c) Assign straight binary state assignment with 3 D-FFs d) Write D A , D B and D C inputs e) Write Output equation for Z 1. Using the SM chart in figure HW15.2 write the equations for D A & D B inputs and all the outputs.

Figure HW15.2 SM chart for problem #3 ANSWERS.

D)  DA (for Q0):  DA = D0 = 0 (for S0)  DA = D1 = 1 (for S1)  DA = D2 = 0 (for S2)  DB (for Q1):  DB = D0 = 0 (for S0)  DB = D1 = 1 (for S1)  DB = D2 = 0 (for S2)  DC (for Q2):  DC = D0 = 0 (for S0)  DC = D1 = 1 (for S1)  DC = D2 = 0 (for S2) So, the inputs for each D flip-flop would be:  For Q0 (DA): 0, 1, 0  For Q1 (DB): 0, 1, 0  For Q2 (DC): 0, 1, 0 e) To write the output equation for Z, you need to consider the conditions under which the output is 1. In the provided state transition table, the output is 1 only when the system transitions from S4 to S1 with X = 0. So, the output equation for Z can be expressed as: Z=S4 ·X’

Step 3/3 SM Diagrams are of three sections: State Box: A state box is a rectangular box that contains a state name, a slice (/), and a discretionary result list. After a state has been relegated, a state code might be placed fresh at the top. Decision Box: A precious stone formed image with valid and bogus branches is a choice box. The articulation in the crate is a Boolean articulation.