Peter Mawhorter
This campus where we’ll be working this semester was historically stewarded by the Nipmuc people, with Wapmanoag and Massachusett people also living in nearby areas. They are no longer the stewards of this land because it was stolen from them, and it’s important that we acknowledge that fact as we start to use this space. These people are still here, you can find their websites and some of them attend Wellesley.
1: This risk is hard to quantify, but many studies suggest it is somewhere between 1/1000 and 1/10 (i.e., between 0.1% and 10%). This planned study has a good discussion and citations, in particular, the 4th paragraph of the “expected key results” section. The risk is significantly higher than for the flu.
Voltage (V) equals current (I) times resistance (R).
Analog
Analog circuits like antennas or speakers have a complex balance of resistance, current, and voltage, which varies over time.Digital
We will study digital circuits, which have defined “high” and “low” voltage values; the exact numbers don’t matter so much.(Once you give a computer scientist a 1 and a 0, it’s game over.)
A prototyping workbench has places to hold wires and chips so you can put them together easily, with internal horizontal and vertical connections. It also has a power supply and things like switches and LEDs built-in.
This is one of our older model workbenches. The next few slides show which components we’ll be using in this class.
The central white area with lots of small sockets is where we’ll attach chips and wires to build our prototypes. Wire tips and the pins of chips should fit snugly into the sockets.
Smaller socket groups around the edges connect to pre-mounted components.
Internally, each row of 5 sockets is connected horizontally, so that components plugged into the same row are in contact. There are also 12 columns of sockets that aren’t part of the 5-socket rows. Each of these columns has internal vertical connections, so that the entire column is connected.
A few of the relevant connections are shown at left; the same pattern applies throughout.
We have set up small red and black jumper wires to distribute power and ground connections throughout the board from the top strips.
Each pair of vertically-connected columns has +5V on the left and ground on the right. This makes it easy to supply voltage or ground at any point on the board by connecting a horizontal row to one of the nearby vertical rails.
The logic indicators on the upper right can be used to display whether the connected wire has high or low voltage. If the LED is on that means the voltage is high, if it’s off that means low. (The newer models have two LEDS to indicate high/low separately.)
Connecting to either of the two horizontal sockets corresponding to a particular LED will supply voltage to that LED.
The logic switches near the lower left corner of the board can be toggled on or off. When on, they supply +5V power to the two corresponding sockets in the nearby strip. When off, those sockets are disconnected.
This picture doesn’t show it, but in our lab, these are pre-connected to ground through a high-resistance resistor. This means that when the switches are off, they will be low-voltage instead of disconnected.
The push-buttons in the lower left work like switches, except that they bounce back to off when released. When off, the top 4 sockets of the nearby strip are grounded, when on, the bottom 4 are grounded instead.
Not shown here, in our lab one of the top sockets for each button is connected to +5V via a resistor. This means that when the button is pressed, the top 4 sockets will be high-voltage, and when it’s released, they’ll be low.
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.
A | B | F |
---|---|---|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
A and B
” or
“A && B
,” now we will write just
“”
for AND and
“”
for OR.
Here are truth tables for NOT, AND, and OR, which you are already familiar with:
NOT | |
---|---|
F = A’ | |
A | F |
0 | 1 |
1 | 0 |
AND | ||
---|---|---|
F = AB | ||
A | B | F |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
OR | ||
---|---|---|
F = A + B | ||
A | B | F |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
Here are truth tables for NAND, NOR, and XOR:
NAND | ||
---|---|---|
F = (AB)’ | ||
A | B | F |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
NOR | ||
---|---|---|
F = (A + B)’ | ||
A | B | F |
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 0 |
XOR | ||
---|---|---|
F = AB’ + A’B | ||
A | B | F |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
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.
Use tools to improve your juggling skills:
A | B | F |
---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
Two functions with the same truth table are equivalent.
F = A’B’ + A’B | ||||
---|---|---|---|---|
A | B | A’B’ | A’B | A’B’ + A’B |
0 | 0 | 1 | 0 | 1 |
0 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 |
Q = A’ + A’B + A’B’ | |||||
---|---|---|---|---|---|
A | B | A’ | A’B | A’B’ | A’ + A’B + A’B’ |
0 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 |