XOR & the Half Adder - Computerphile 

Darren Landrum but would the members play anything else than keys?

MAsYna Tutnga

Mi do nit czree

He is on

Dlaczego?

yep

gotta go fast

same

ikr, youtube has taught me more about for major than the teachers have at my uni for sure.

YES! I agree!!!

@PIYUSH YADAV Someone doesn't understand hyperbole.

I am currently in the process of binge watching this channel.

Lol

ÀAAaaàÀà@@asaffisher8890

i have like two stacks of torches though...

Same.

I can’t believe how Smart the guy is. How much is in that head.

yeah you could but obviously you're not :P

6502 on my side, they chose EOR, a carry over from Motorola's 6800 instruction set when Chuck Peddle skunk-worked MOS Technology from them; same instruction though.

Fortunately I only had to build a 32bit ALU in verilog.

Derek Leung Just got out of a 16 bit carry lookahead adder in VHDL

Heh, do "From nand to tetris" -that's fun. "Oh, just build a computer"...

Markus Mines I have done a small amount of transistor logic using 2N3904 transistors, but they are rated for slightly higher current (NPN, 250mA);also some 2N2222A transistors (NPN, 800mA);and MJE3055T (NPN, 8A);and IRF540N (N-MOSFET, 33A).usually, the smaller transistors are for signaling and logic, and bigger transistors are for driving loads (such as electric motors).a lot of it is mixed digital and analog electronics, with parts operating at different voltages (3.3v, 5v, 12v, and sometimes higher, ex, 15v-24v).transistor logic isn't really fun, much easier to do any non-trivial logic using microcontrollers or a Raspberry Pi or similar... (leaving the discrete electronics mostly to non-logic tasks).wouldn't look forward to building complex digital circuits with transistors.most complex I built was a circuit for running bipolar stepper motors with transistors (sadly/ironically, thus far works better than my attempts at using driver ICs).NPNs are good for small digital circuits, and have good properties for analog, but the drawback of generating considerable amounts of heat. a few of my NPN-based circuits (simple analog logic) are actually insulated with silicone caulk and run while submerged in water for this reason, and may actually cause the water to start boiling off the transistors while running (yes, actually built the thing to run underwater...).MOSFETs, however, are more expensive and don't deal as well with analog signals (in a simple sense, they like to behave more like on/off switches).well, and of course, a lot of this stuff is wire-wrap (typically with 24 gauge wire, or thicker for higher loads), and a lot of resistors, capacitors, and a few ICs and other things in the mix as well...but, it is worthwhile I guess...

+Brendan Bohannon The npn transistors you use for digital logic that give off heat, are you using resistors for that? It shouldn't overheat like that for simple digital logic.

I did a 24 bit full - adder, why 24? Because it got real boring after 23... ;)

hmmm, without mod, I doubt, you would have been out of chunk loaded area :)

Ya, you're probably right, must have been half-adders, I don't remember, my bad (Still got boring after 24):)

XD

kanethornwyrd On second thought, I think I got a full adder to work in like 9x5 blocks or something. But I might be mistaken ;)

Yeah, whatever input goes through it always comes out much larger.

lol

a set of gateS; And, Or, Xor, Not, Nand, & Nor.

And gate , Or gate, Nor gate, nand gate,.........,bill gate 😂

😂😂😂

wishcraft4u2 LOL I had to pause the truth table a few times to make sure I understood it all too. He's an excellent teacher!

hehe i can get it if i watch for like 2 to 4 times

Blame camera's pos

I know it's 5 years later, but the problem with this idea is that an or gate in itself is 4 nand gates(you need to invert both inputs and output) or 2 nor gates(invert the output). There is no way to electronically do an or gate directly. So while you are correct in a sense that an half-adder can be done in three operations, unfortunately one of those operations requires 4 gates to do. TL;DR Yes, as long as you ignore the fact that the OR gate is actually 4 NAND gates, since we can't make an OR gate directly, unlike a NAND or NOR gate.

@Connor Gaughan Actually, that’s (A∨B)∧¬(A∧B). ∧ and ^ are different symbols.

we did? of course we did! .>

Gg

tl;dr: a⊕b = (a+b)&¬(a&b) and a⊕b = (a&¬b)+(b&¬a) you can actually construct xor from and and or by starting with an approximation and refining it. I can start with approximating a⊕b with a+b. this gets 3 out of four correct. I can then look at what the incorrect one should be(0) and what conditions make that case(a=b=1) I can take the result of my first approximation and and it with 0 to force it to be zero, but I only want this to happen for this fourth case. so now I have a⊕b as (a+b)&c where c is zero if and only if a=b=1. sounds a lot like not and, doesn't it? then we have a⊕b = (a+b)&¬(a&b) another way to construct boolean functions for any arbitrary truth table is to find all of the cases where the result is one, create an expression that is only true under those circumstances, and or those expressions together. that ends up with a⊕b=(a&¬b)+(b&¬a)

faissialoo well here's a XOR in Boolean. A⊕B = (A∨B) ∧ ¬(A∧B).But if you're gonna make a XOR in Minecraft I'd prefer (A ∧ ¬B) ∨ (¬A ∧ B) as it's simpler to understand.The second one is easier to follow in my opinion. ∨ = OR ∧=AND ¬=NOT ⊕=XOR

Merthalophor every logical function is derived from OR and NOT. All computational can be done with just those two and all other gates are derivations of them.

Nickster258 Both work. You're _wrong_. "All other gates *can be devirated from them".

I think a carry in, is if you carry 1 but in he number, so you have to add it to the next column wich already exists. But i'm not sure.

I'm pretty sure they stuck to two inputs for simplicity, and because it ties into their earlier logic addition content. Besides, a 6 input XOR is just five regular two input XOR gates stuck together. You start by putting three pairs through, and getting three outputs. You put outputs 1 and 2 through another XOR, and then take that result, along with you third output through the last XOR. I'm sure there is a smarter (at least less transistor heavy) way to do it, but you don't need dedicated 6 input XOR gates, just like you don't need more than two inputs on any other logic gate. AND and OR gates combine into their respective 6 input versions the same way as XOR.

Improbabilities You are certainly right.

Gareth Dean Multiplexers. Binary number on input defines which of output wires is active. Of course that consists of applying technically separate logical function on inputs for each output wire.

kasuha Cool, thanks.

kasuha What you described is a Decoder. A Multiplexer has one Data input, n select inputs and 2^n outputs. The binary number on the select input defines which output the input signal is forwarded to.

swiss It's a while since I stopped having fun with designing hardware circuits, I'd swear we used to call these parts that but apparently I was wrong. It's even a demultiplexer actually. I'd guess we were just lazy to use such a long name for a part we were using all so often.