ECE 171: Introduction to Digital Circuits

Fall 1999

Rev: 10.19.99

Lecture Notes 7

Last Time

• Data Sheets from homework
• Tristate Outputs
• Wired Logic
• Capacitors
• Timing Diagrams

This Time

• Capacitors
• Translations
  • Logic Diagrams
  • Truth Tables
  • Boolean Expressions
  • Sum of Products (SOP)
• Review for Midterm

Capacitors

• Key idea is that they resist rapid changes in voltage.
• They act like a charge storage device that can temporarily supply power to a circuit.
• The application that we've discussed so far is to regulate the power supply voltage of gates. When all of the gates switch simultaneously the capacitor helps keep the voltage constant.

Logic Analysis/Synthesis

• Previously we discussed how to construct simple truth tables, logic diagrams, and boolean expressions.
• Now we're going to discuss this in more depth.
• This marks a turning point for the next couple of weeks where we will move away from the physical devices and more towards the mathematics of digital circuits.
• Today we will discuss how to make the following "translations"
  • Logic Diagram to Boolean Expression
  • Boolean Expression to Logic Diagram
  • Truth Table to Boolean Expression
  • Boolean Expression to Truth Table
  • Logic Diagram to Truth Table
• Note that the three representations of a logic "block" are equivalent, but not all of them are unique. In particular:
  • Boolean expression is not unique
  • Logic Diagram is not unique
  • Truth Table is unique

Logic Diagram to Truth Table

• Start with the inputs
• Count the number of inputs
• Truth table will have 2^N rows where N is the number of inputs
• Label intermediate nodes
• Memorize the truth tables for the 8 basic logic gates

Draw a three input logic circuit with three gates. Have students pick the gates. Label the intermediate nodes and fill out the truth table.

Logic Diagram to Boolean Expression

• Start with the inputs
• Label intermediate nodes
• Work from inputs to output
• Use substitution

Draw a different three input logic circuit with three gates. Have students pick the gates. Label the intermediate nodes.

Boolean Expression to Logic Diagram

• Devide the expression into blocks
• Use substitution
• Start with the output

Have students pick the gates as you write a complicated expression using three or four inputs. Devide the expression into chunks are draw the logic diagram starting with the outputs and working towards the inputs.

Boolean Expression to Truth Table

• Count the number of inputs
• Use substitution
• Put the subexpressions in the truth table
• Work from the subexpressions nearest to the inputs to the output

Have students help pick the relationships in a complicated expression of three inputs. Label subexpressions. Write out truth table and fill it in slowly working from left to right.

Truth Table to Boolean Expression

• The two most common methods are called Sum of Products (SOP) and Product of Sums (POS)
• Today we will only talk about SOP. Will discuss POS next week.

Write out a three-input truth table with three outputs F1, F2, and F3. For each output pick a single row that has a one. Show students how to write a boolean expression for a function F1 that is 1 for only one row in the truth table. Repeat this for the other two functions, F2 and F3. Add a column to the truth table that has three ones where the ones from each function were. Show students how F = F1 + F2 + F3. Use substitiution to get the final expression.

Show how this can be implemented easily using 3 AND gates, 1 OR gate, and some inverters.

Show also how this can be implemented with just NAND gates.

Exam

• 5 Questions - multiple parts
• Calculators are allowed
• Covers book Chapters 1-5 selectively. Nothing on transistors, mixed logic (assertion levels and * notation), or how to operate lab equipment.
• You may bring 2 single sided sheets of notes or one double sided sheet of notes.
• You will be allowed exactly 100 minutes to take the exam.
• The afternoon exam will be given in Neuberger Room 11 (in the basement near the North side).
• Do not forget to bring your 6-digit code. Email me if you've forgotten already.

Review Material

• When you connect the outputs of open collector or open drain devices, it forms an AND. The book sometimes states that this is an OR function or a NOR function, but logically it is an AND and you should treat it as such.
• You are not expected to know about active highs, active lows, negative logic, mixed levels logic, or assertion levels. You do not need to know about the * notation.

Review of Exam Topics

Click here for the list.