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CS 315-01 Lecture/Lab — Meeting Summary (Fall 2025)

Date/Time: Oct 16, 2025, 08:14 AM Pacific
Meeting ID: 886 4953 2573

Quick Recap

The session covered core digital design concepts: - How electrical values represent binary data (0s and 1s) - Basics of logic gates and circuit types - Techniques for building combinational circuits: - Truth tables - Boolean equations - Sum of Products (SoP) - Using design tools to construct and optimize circuits - Assignment: build an 8-bit ripple-carry adder - Reminder: Lab 8 deadline; upcoming topics include subtractors and additional combinational components

Next Steps

  • Students: Complete and submit Lab 8 to their repository by Monday night.
  • Greg: Send repository links to students today.
  • Greg: Fix the Autograder repository to resolve error messages.

Summary

Digital Design Fundamentals

  • Electrical values encode binary data, forming the basis of modern processors.
  • Logic gates can express any computation.
  • Distinction between:
  • Combinational logic: acyclic circuits with outputs depending only on current inputs
  • Sequential logic: circuits with cycles that store state

Combinational Logic and Circuit Design

  • Overview of designing circuits to perform specific functions.
  • Introduction to an 8-bit adder.
  • Systematic construction using basic gates and the Sum of Products (SoP) method:
  • Create a truth table
  • Transcribe to a Boolean equation
  • Build the circuit
  • Example: determining even/odd for a 3-bit number using simple counting and Boolean logic.

Truth Table Construction Techniques

  • For three inputs, systematically enumerate all input combinations.
  • Identify rows producing desired outputs and apply the SoP algorithm.
  • Emphasis on understanding the technique before using automation tools.
  • Derive the Boolean equation for “odd” by negating the equation for “even.”

Digital Circuit Design Tutorial

  • Building circuits from Boolean equations:
  • Define inputs
  • Configure AND gates with varying input counts
  • Use inversion bubbles appropriately
  • Wiring best practices: lines that cross without dots are not connected.
  • Notes:
  • Autograder installation issues were acknowledged; a repository fix is pending.
  • Recommended reading: first 20 pages of the digital tool’s manual.
  • Suggested using keyboard shortcuts for efficiency.

8-bit Adder Design Overview

  • Review of a Sum of Products problem from Lab 8:
  • Use truth tables and equations to find max values per input combination.
  • Importance of adhering to naming conventions for inputs, outputs, and files in auto-graded labs.
  • Next design milestone: build an 8-bit adder following a short break.

Combinational Circuits for Addition

  • Start with a 1-bit full adder; scale to an 8-bit ripple-carry adder.
  • Connection to grade school arithmetic implemented via circuits.
  • Emphasis: addition is foundational to computer operations.
  • Concept of propagation delay: outputs stabilize after carries ripple through the adder chain.

1-Bit Full Adder: Design Demonstration

  • Construct a 1-bit full adder using standard gates.
  • Optimization techniques and component customization:
  • Colors, sizes, orientations
  • Save circuits as subcircuits and refine layouts for clarity and reuse.

8-bit Ripple-Carry Adder

  • Use splitter/merger components:
  • Split 8-bit inputs into single bits
  • Recombine outputs into an 8-bit result
  • Abstraction enables building larger adders (e.g., 32-bit, 64-bit) from 8-bit blocks.
  • Upcoming topics:
  • Building a subtractor from an adder
  • Additional combinational components for processor design
  • Reminders:
  • Lab 8 due Monday night
  • Review the digital tool’s documentation for familiarity and best practices