Digital Logic Design Lecture 28. Announcements Homework 9 due on Thursday 12/11 Please fill out Course Evaluations online. Final exam will be on Thursday,

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Digital Logic Design Lecture 28

Announcements Homework 9 due on Thursday 12/11 Please fill out Course Evaluations online. Final exam will be on Thursday, Dec :30- 12:30 in CHE 2118 (our regular classroom). Shang will hold a review for the final exam in AVW Vote on time for review session: – Friday, 12/12 from 11am-12:15pm – Friday, 12/12 from 12:30pm-1:45pm

Agenda Last Time: – Modeling Clocked Synchronous Sequential Network Behavior (7.3) This time: – State Table Reduction (7.4) – The State Assignment (7.5) – Completing the Design of Clocked Synchronous Sequential Networks (7.6)

Determining Equivalent Pairs of States

Example of State Table in Which State Reduction can be performed

Algorithm for Determining Equivalent Pairs of States Uses an implication table

Algorithm for Determining Equivalent Pairs of States

Example of Algorithm

Algorithm for Obtaining the Equivalence Classes of States

Example for Implication Table

Constructing the Minimal State Table

Next Step: Constructing Transition Table from State Table A binary code representation for the states of the state table is selected. This is referred to as the state-assignment problem. Different state assignments result in realizations of different costs. – We want to find a state assignment that minimizes the cost of the network realization.

State Assignment

Simplest Approach

Next-State and Output K-maps

Guidelines for Obtaining State Assignments Define two states as being adjacent if their binary codes differ in exactly one bit. Two input combinations are adjacent if they differ in exactly one bit.

Guidelines for Obtaining State Assignments Rule I: Two or more present states that have the same next state for a given input combination should be made adjacent. Rule II: For any present state and two adjacent input combinations, the two next states should be made adjacent. Rule III: Two or more present states that produce the same output symbol, for a given input combination should be made adjacent (only needs to be done for one of the two output symbols).

Rationale for Guidelines

Example

Next consider Rule III: Look at present states that produce output symbol 1 on the same input.

State Assignment Map K-map for the state variables in which each cell of the map denotes a combination of the binary digits that can be assigned to a state of the sequential network.

Transition Table Using the state assignment map and state table, a transition table is constructed.

Transition Table K-maps for next-state and output functions.