Important Policies

• No food or drink
  • You may step out for a snack/sip, and we’ll have a break.
• Masks are required
  • (Due to the prevalence of asymptomatic infections, and the as-yet-unquantified nature of the risks of COVID-19.)

Course Parameters

• Pre-lab exercises will be in Google docs, or in Gradescope
  • Pre-lab exercises are individual
  • Share docs w/ partner & instructor
• I will assign different partners each lab
• Grade is based on pre-lab assignment (30%) and in-lab work (70%), or just in-lab work if there is no assignment

Partner Work

• Be kind to each other (yes, even when you’re tired)
• Enhance each others’ learning
• You’ve had practice at this

Expectations

• You’re now full-fledged CS majors
  • Capable of independent learning
  • Will ask questions when you need to
  • Will be responsible for meeting deadlines, doing prep work, etc.
• You will succeed and thrive in this class, and you’ll go on to do great things with this knowledge.

Growth Mindset

• When you’re having trouble, identify why and what you need to practice to improve.
• Don’t limit your own potential by buying into the belief that you are either “bad at” or “good at” a subject.
• This class is hard in order to make you grow strong (but hopefully in a gentle way).

Logging In

• Use your Wellesley username/password for Windows
• Use your CS Department username/password for Linux
  • (you set this up in CS 111 or more likely CS 230, if you didn’t just do it this week)
• Mash F12 when it boots to get to the boot menu for some machines

Setup

1. Find your partner.
2. Log in to Windows on at least 1 machine.
3. Open up a browser an navigate to the class website’s lab section.
   • Scroll down to the bottom to find Lab 1
   • Open up these slides and also the Lab Notebook
4. Make your own copy of the lab notebook, and share it with your partner and with me (pmawhort@wellesley.edu).

What is Electricity?

• Electricity = the movement of electrons in a material
  • Movement happens because of extra electrons in one place, or extra “holes” in another place, or both.
  • Electrons are so fast. Really, just so fast.

What is Electricity?

• We measure the surplus or deficit of electrons in relative terms
  • This is voltage (V, measured in Volts), and is always a difference between two points.
  • When unimpeded, the flow of electrons quickly reduces voltage to 0.
• Rate of flow is called current, (I, measured in Amps)
• All materials resist the flow of electrons
  • This is called resistance (R, measured in Ohms = Ω)

What is Electricity?

• Materials that have low resistance are called “conductors”.
  • The resistance of a copper wire is basically 0 (it’s around 1 Ω per 1000 feet of wire, depending a bit on thickness).
• We use resistors with specific Ohm ratings to create resistance in our circuits, often ~1.8 kΩ.
• Your body has a resistance value anywhere from 300-100,000 Ω
• Air has resistance of 1.3-3.3×10¹⁶ Ω (until about 21 kV/cm)

Ohm’s Law

$V = I \times R$

Voltage (V) equals current (I) times resistance (R).

• More voltage → more current
• More resistance → less current, since $I = \frac{V}{R}$
• Zero resistance = infinite current (!)

Ohm’s Law

• Conventions are hard to change, current is shown backwards from the flow of electrons (we don’t care).
• For our purposes, an open switch (meaning electricity has to jump across air) has infinite resistance: no current flows.
• We also don’t care about the resistance of our wires, they are effectively 0.
• A “short circuit” means a circuit with negligible resistance. Current becomes very high, until the circuit destroys itself.

Digital vs. Analog

Digital vs. Analog

• A typical digital circuit uses just 5 volts, and might define “high” as anything above 3 volts, and “low” as anything below that (more detail).
• Only minimal current may be necessary for the circuit to function, as long as the correct voltage differences can be achieved.
• Using “high” and “low” we can represent True and False, or 1 and 0.

(Once you give a computer scientist a 1 and a 0, it’s game over.)

Gates and Truth Tables

Boolean Algebra

• Before, you might write “A and B” or “A && B,” now we will write just “$AB$” for AND and “$A + B$” for OR.
  • Basically, AND is multiplication and OR is addition.
  • $1 \times 1$ is 1, but anything $\times 0$ is 0.
  • $0 + 1 = 1 + 0 = 1 + 1$ (if you can’t go above 1).
  • Use ’ for NOT, or write a bar above: A’ or $\overbar{A}$

Boolean Algebra

• A minterm is an AND of all of the inputs to a function, possibly with NOTs. The four minterms of two inputs A and B are: AB, A’B, AB’, and A’B’.
• A maxterm is an OR of all inputs, possibly negated. The four maxterms of two inputs A and B are:
  A + B, A’ + B, A + B’, and A’ + B’.

Basic Functions

Here are truth tables for NOT, AND, and OR, which you are already familiar with:

Basic Functions

Here are truth tables for NAND, NOR, and XOR:

Basic Functions

• Why NAND, NOR, and XOR?
  • NAND and NOR are easier to build in a circuit than AND and OR, as we’ll soon see.
  • XOR is quite useful in a number of applications, including cryptography.
  • As the formulas show, NAND, NOR, and XOR can be built out of AND, OR, and NOT.
  • Alternatively, AND and OR can be built from NAND, NOR, and NOT.

Gate Symbols

Aside: Mental Juggling

Aside: truth tables present information clearly, but they’re hard to read, and it’s harder to keep them in your head as you then try to apply them to each other or think through a circuit.

This class will repeatedly strain (and also develop) your ability to mentally juggle multiple steps of translation between different representations and parts of a system.

Aside: Mental Juggling

Use tools to improve your juggling skills:

• Keep references handy, ideally visible without having to even click or turn a page.
• Practice to internalize key info, like the basic truth tables.
• Keep scratch paper or a scratch file handy to write things out when your mental stack is out of space.

Sum-of-Products

Sum-of-Products

• Any boolean function can be expressed as a sum-of-products, which only needs NOT, AND, and OR.
• If we had circuits that could produce these functions, we could put them together to compute anything.

Equivalence

Two functions with the same truth table are equivalent.

Equivalence

• Use Boolean algebra to find/prove equivalence.
• Find ways to make the same circuit with fewer or cheaper gates.

Transistors

• To be able to build NOT, AND, and OR gates in a circuit, there has to be a way for voltage or current in one place to manipulate the flow of current or the difference in voltage somewhere else: a switching mechanism.

• Early switches were big (vacuum tubes) but transistors represent the culmination of decades of research into making them smaller.

• A modern transistor can be as small as 5 nanometers, with 10s of billions packaged on a singe chip.

Transistors

• When voltage is present at the trigger side of a transistor, current may flow through, but if no voltage is present, current may not flow.
• To create a NOT gate, connect input A to the trigger, and output F to the wire leading into the transistor’s channel. (simulation link)
  • When A is high, the current flows across the transistor, draining away voltage above the transistor.
  • When A is low, current cannot pass the transistor, and gets bottled up behind it, creating high voltage at the output.
  • Resistors prevent a short circuit in either state.

Integrated Circuits

Integrated Circuits

Protoboards

Building a Gate

Simulation

• In addition to building circuits, we’ll be simulating them using LogicWorks. It’s available in Windows on the lab machines.
• For simple circuits, you can also use the Falstad circuit simulator which shows voltage and current flow, but has fewer options for labelling, checking timing, and building more complex circuits.