Chapter 15 - Digital Logic #
| Binary (0b) | Hex (0x) | Decimal |
|---|---|---|
| 0000 | 0 | 0 |
| 0001 | 1 | 1 |
| 0010 | 2 | 2 |
| 0011 | 3 | 3 |
| 0100 | 4 | 4 |
| 0101 | 5 | 5 |
| 6 | 6 | |
| 0111 | 6 | 7 |
| 1000 | 8 | 8 |
| 1001 | 9 | 9 |
| 1010 | A | 10 |
| 1011 | B | 11 |
| 1100 | C | 12 |
| 1101 | D | 13 |
| 1110 | E | 14 |
| 1111 | F | 15 |
lineart by https://merveilles.town/@chirrolafupa, I (Vega) filled it in and turned it into a gif.
To access the original line art, use a gemini browser to go to gemini://caracolito.mooo.com/coloring-computers/
[Todo, insert intro about Minecraft redstone]
What is digital logic? #
ignoring the analog world (10%/90%)
Truth Tables, K-Maps #
min/max terms, Don’t cares, SOP/POS, multiple out
[TODO] http://nandgame.com
Basic Logic Gates #
[TODO] truth tables, circuit symbol, discrete logic symbol for all.
Not #
| Input | Output |
|---|---|
| 0 | 1 |
| 1 | 0 |
Truth table, transistor implementation pmos/nmos, cost, power consumption at switch
AND #
A∧B, AB,
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
NAND #
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Or #
Nor #
Exnor #
Xor #
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Exor #
Transmission, #
Mux #
Demux #
Encoders #
Basic combinational logic #
propagation delay, fan in/out, POS/POS
2’s Compliment, Floating Pt, Math #
overflow, carry, ripple, fast, mul, shift-and-add mult, divider,
Latches and Flip Flops #
SR, Dl, edge triggering, Dff, Tff, JKff,
Registers #
Counters #
Making Some Circuits #
There’s a ton of simulators out there for making simple circuits educationally, but most sorta suck, so I’m going to delve right into something fun: Minecraft
If you don’t own MineCraft and can’t afford it, MineTest with mesecons is an option. It’s… not great. (sorry MineTest team, I still love what you’re doing <3 ) But it is Open Source. If you’re using Arch Linux (and updates haven’t broken things since writing) you should be able to install
MineTestfrom the community repo andmesecons-gitfrom the AUR.
More Digital Logic resources #
We’ll come back to look at more complex digital logic in chapter 28 “Let’s try out programmable logic” and 29 “Let’s make our own CPU” , but if you’re hungry for even more, here are some resources