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CS 315-02 Lecture/Lab — Meeting Summary (Fall 2025)

  • Date: Oct 16, 2025
  • Time: 02:55 PM Pacific Time (US & Canada)
  • Meeting ID: 868 6589 0521

Quick Recap

The session covered core digital design and logic concepts: - Basics of digital circuits and logic gates (AND, OR, NOT) - Difference between combinational and sequential logic - Constructing Boolean equations and truth tables using the Sum of Products (SoP) method - Building foundational circuits (1-bit full adders, 8-bit ripple-carry adders) - Emphasis on abstraction, clean organization, and proper circuit structure

Next Steps

  • Students:
  • Complete Lab 8, Part 2: Use the Sum of Products technique to build a circuit that computes the maximum of two 2-bit numbers.
  • Build an 8-bit Ripple-Carry Adder by chaining eight 1-bit Full Adders.
  • Keep designs organized: avoid overlapping text and messy wiring.
  • Use exact input/output names as specified in the lab requirements.
  • Read the first 20 pages of the Digital tool documentation (keyboard shortcuts and tutorial basics).
  • Greg:
  • Update the Autograder README with simplified installation instructions.
  • Post the simplified Autograder installation steps on Campus Wire.

Summary

Digital Logic and Circuit Design

Greg outlined how digital circuits use gates to perform computation and scale up to complex systems (e.g., processors, FPGAs). He distinguished: - Combinational logic: acyclic; outputs depend only on current inputs. - Sequential logic: involves cycles/state; will be covered next week.
The near-term goal: build an 8-bit adder.

Boolean Abstraction for Circuit Design

To manage complexity at scale, Greg emphasized abstraction and the Sum of Products method: - Define behavior with a truth table. - Derive Boolean equations using SoP. - Translate equations into circuits systematically. Example discussed: determining parity (even/odd number of 1s) for a 3-bit input.

Boolean Equation Creation Method (Sum of Products)

Process overview: 1. Build a truth table for all input combinations. 2. Identify rows where the output is 1. 3. Create product terms for those rows (invert inputs as needed). 4. OR the product terms to obtain the final Boolean equation.
This approach is reliable for both function definition and circuit implementation.

Digital Circuit Design Demonstration

Using the digital design tool, Greg demonstrated: - Creating AND gates with multiple inputs and using inverters (bubbles) for negation. - Drawing clean, symmetric wiring and organizing components. - Leveraging the documentation’s first 15–20 pages for tutorials and shortcuts.

Circuit Design and Autograder Updates

  • Demonstrated circuits for even/odd detection and how to run the autograder.
  • Addressed installation issues; proposed a simpler method using UV.
  • Committed to updating the Autograder README and posting instructions on Campus Wire.
  • Noted that Lab 8, Part 2 focuses on a Sum of Products problem.

2-bit Max Function: Truth Table and SoP

  • Construct a 16-row truth table for all combinations of 2-bit inputs A and B.
  • Derive separate SoP equations for output bits R1 and R0.
  • Follow the exact naming conventions provided in the problem statement.

Optimizing with De Morgan’s Law

  • Discussed using De Morgan’s Law to simplify/rewrite equations and reduce product terms.
  • Emphasized that while brute-force SoP works, optimizations can improve efficiency.
  • Noted varied student backgrounds; deeper optimization techniques to be covered later.

Building a Full Adder Circuit

  • Clarified half adder vs. full adder:
  • Half adder: handles two input bits.
  • Full adder: includes carry-in and produces sum and carry-out.
  • Recommended deriving the full adder’s Boolean expressions by enumerating all input combinations—useful preparation for subsequent work.

One-Bit Full Adder: Gate-Level Construction

  • Step-by-step demonstration using AND/OR/NOT gates to realize the full adder.
  • Reinforced that while optimization matters, the course focuses first on solid foundational techniques.

Binary Addition and Ripple-Carry Adder

  • In binary addition, each bit position produces a sum and potentially a single carry bit (0 or 1).
  • An 8-bit Ripple-Carry Adder chains eight 1-bit full adders:
  • Each adder consumes Ai, Bi, and carry-in; outputs Si and carry-out.
  • Carry-out ripples to the next stage, mirroring grade-school addition.
  • Highlighted the power of abstraction: reuse validated components.

Tooling and Organization for Multi-bit Circuits

  • Demonstrated building an 8-bit adder using:
  • Splitters/mergers to handle multi-bit buses.
  • Clean alignment of inputs/outputs and tidy wiring practices.
  • Noted upcoming transition to sequential logic in the following weeks.