15 Digitallogic

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
logicloop

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 MineTest from the community repo and mesecons-git from the AUR.

Minetest Circuit Challange

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


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