Binary. How does it actually work?

[Siri137]

Oh look. There's a smiley-face! :)

You know, those ones and zeros that computers apparently use, and that geeks use to communicate with each other. I've looked into it, into the rules, but to me they just do not make any sense whatsoever.

Updates

1 mo

You've given some good answers, but it still doesn't make any sense to me. I guess I should avoid a career in computing then, because I probably wouldn't have the knack for it. :(

[RebelinSteel]

If used within digital electronics, then a good starting point is that with a 1 being high and a 0 being low, it just means one is a higher level, you can have say 3.2v as 0 and above 3.2 as a 1. This is useful with logic gates that rely on the status of an input to give an out put, logic gates act in different ways based on the type of gates, AND, NAND gates, with the latter being classed as a universal gate.

https://de-iitr.vlabs.ac.in/exp/realization-of-logic-functions/theory.html#:~:text=1)Nand%20gate%20as%20Universal%20gate&text=This%20gate%20can%20have%20minimum,also%20called%20as%20universal%20gate.

Boolean Algebra also comes into using Binary https://www.electronics-tutorials.ws/boolean/bool_6.html

A very simple digital setup would be to show if a door was open or closed, that would be a 1 or 0?

now imagine if you had to have a logic that said the final door is only open if the first door is open and second door is closed. Then increase the number of doors that need to be open and closed to say 80 doors and a mix of open or closed.

https://www.geeksforgeeks.org/boolean-algebra/

Then add in Karnaugh mapping and truth tables

https://www.geeksforgeeks.org/introduction-of-k-map-karnaugh-map/

https://maker.pro/blog/what-are-logic-gates-and-why-are-they-important

https://www.electronics-tutorials.ws/binary/bin_1.html

Then with an Adder or Half Adder you start putting the logic gates together and using outputs https://en.wikipedia.org/wiki/Adder_(electronics)

Another key item in the Binary Electronics world is the Op Amp.

https://www-robotics.cs.umass.edu/~grupen/503/SLIDES/OpAmps/opamps.html

https://www.electronics-tutorials.ws/opamp/opamp_1.html

the modern world operates on 1s and 0s, all electronic devices use binary, the development of a new electronic circuit or device, is built on using components that basically produce a 1 or 0.

obviously there is far far more to it,

http://bibl.ica.jku.at/dc/build/html/basiccircuits/basiccircuits.html#:~:text=Digital%20circuits%20are%20compositions%20of,%2C%20decoders%2C%20and%20memory%20elements.

a basic digital circuit will use transistors, capacitor, resistors etc, however a microprocessor (a chip) with use millions of these to 100s billions, an Nvidia Ai chip has 200 billion.
The highest transistor count in a single chip processor as of 2020 is that of the deep learning processor Wafer Scale Engine 2 by Cerebras. It has 2.6 trillion MOSFETs in 84 exposed fields (dies) on a wafer, manufactured using TSMC's 7 nm FinFET process.

the average smart phone has 10 billion transistor circuits.

these all operate on binary / digital

[RebelinSteel]

@siri137 Ref update, you either do or you don’t
(Binary joke)

[bolverk]

What is binary?
Binary describes a numbering scheme in which there are only two possible values for each digit -- 0 or 1 -- and is the basis for all binary code used in computing systems. These systems use this code to understand operational instructions and user input and to present a relevant output to the user.
The term binary also refers to any digital encoding/decoding system in which there are exactly two possible states. In digital data memory, storage, processing and communications, the 0 and 1 values are sometimes called low and high, respectively. In transistors, 1 refers to a flow of electricity, while 0 represents no flow of electricity.
American Standard Code for Information Interchange (ASCII) is the code used for text files in computing.
Binary explained
The binary numbering system was refined in the 17th century by Gottfried Leibniz. In mathematics and in computing systems, a binary digit, or bit, is the smallest unit of data. Each bit has a single value of either 1 or 0, which means it can't take on any other value.
Computers can represent numbers using binary code in the form of digital 1s and 0s inside the central processing unit (CPU) and RAM. These digital numbers are electrical signals that are either on or off inside the CPU or RAM.

https://www.youtube.com/watch?v=wgbV6DLVezo

[IslaTheWitch]

It's just one of many methods to code the information. It's cheaper to code using 0 and 1 than many chars like alphanumeric.

In general binary code numbers. You read it always from the end every 0 or 1 codes value of 2^x where x is a number from 0 to n, where n is number of positions for coding - 1

1101

(2^3)*1 + (2^2)*1 + (2^1)*0 + (2^0)*1 = 8 + 4 + 0 + 1 = 13

[KostasKouvalis]

That made my head hurt. While the actual math isn't that complicated I still don't understand what "n" represents, and why (2^3)? Why not just write 8?
So 4 digit sequences represent one number like 13? If they already know that, why bother with the equation?
And why always 2^? Why not 5^ for instance?

I guess I'm more confused about what the information actually means, because the equations are easy even for someone like me who struggles with math.

by the way, can you check your PM?
Wysłałem ci ćos.

[IslaTheWitch]

@KostasKouvalis g@g slackuje z powiadomieniami o prywatnych wiadomościach, zajrzę wieczorem, póki co cieszę słońcem :D

[IslaTheWitch]

@KostasKouvalis power of 2 because only it allow you to code any integer...
3^0 = 1
3^1 = 3
how you want to get 2 out of it?

[KostasKouvalis]

Aha! Ja też właśnie ostatnio mam problemy za wiadomominiem o PMach.

Okay. Nie ma sensu mi próbować to rozszyfrować🤣

Tak? To z korzystaj ze słońca dopóki to masz😉

[Siri137]

@KostasKouvalis So you actually are Polish, not Greek. And n usually represents any integer, or whole number, although in physics (optics) it means refractive index, but perhaps she already explained that to you in Polish.

[KostasKouvalis]

I've told you like 5 times already that I'm Polish. Kostas Kouvalis is just an alias

How do you know what she was explaining to me? 😋

[Siri137]

@KostasKouvalis Okay, I get. Polish. This time I won't forget. But... why are you using a GREEK alias, and not a Polish one?

[Siri137]

@KostasKouvalis Well, what else would you have been discussing? Sex? ;P

[KostasKouvalis]

It's a long story. Does it really matter?
Either sex, feet or politics

[KostasKouvalis]

Or our friend 😉

[KostasKouvalis]

I guessed you missed my Polish cover of "La Vida Loca"😂

[Siri137]

@KostasKouvalis No, it doesn't matter. I was just curious about it, that's all.

[KostasKouvalis]

Maybe later. I thought I told you before

[Siri137]

@KostasKouvalis So why does she write 2^3? Why not just 8? That's what 2^3 is, so why not keep things simple?
You see, this is what I HATE about maths. Mathematicians seem to get high on making things as complicated for both themselves and others as they possibly can. I prefer simplicity. Keep things as simple as one possibly can. I don't need added complexity in my life. Life is complicated enough as it is.

[KostasKouvalis]

For those "solve for X" problems, I would always use trial and error. It was always fun when I had to show my work😂 Technically the teacher couldn't mark it wrong, though I did have one teacher who would mark you wrong if you didn't use HER methods, even if there were easier ones.

[goaded]

You know how normal numbers go 0 1 2 3 4 5 6 7 8 9 10 11 12? When you get up to a number ending with 9 and add one, you go back to 0 and add one to the column to the left, until you don't. e. g. 999 + 1 = 1000.

Binary numbers can only use 0 and 1, so when you add 1 to 1, you go back to zero and add one to the column to the left. They go: 0, 1, 10, 11, 100, 101, 110, 111, 1000...

Memory in a computer has a fixed size, generally 64 bits (binary digits) these days. Choosing 8 bits instead, the numbers go:

00000000 = 0

00000001 = 1

00000010 = 2

00000011 = 3, etc.

[Siri137]

Why isn't three 00000100? And four 00001000?

[IslaTheWitch]

Because every position is coded by power of 2
so three is:
2^1 + 2^0 = 2 + 1 = 3
Four:
2^2 + 0 + 0 = 4

[goaded]

@IslaTheWitch Exactly. Each column, rather than being units, tens, hundreds, thousands, etc. are units, twos, fours, eights, sixteens, etc.

01101100 is 0 * 128 + 1 * 64 + 1 * 32 + 0 * 16 + 1 * 8 + 1 * 4 + 0 * 2 + 0 * 1

[goaded]

" Why isn't three 00000100? And four 00001000? "
Because three is 2 + 1, 2 is 10, and adding 1 to 0 is 1, making 11.

To add one more, to make four, 1 + 1 = 10 (so 0, carry the one), same for the next column, so 11 + 1 = 100.

[goaded]

Honestly, I don't know how relevant binary is to the average programmer any more. Back in the day, we'd have to worry about overflowing a byte (256) or a word (65536), but 64 bit words can carry pretty much any practical number.

How about thinking of it another way? Imagine you're working in base 10, normal arithmetic, but every one is a five.

0 + 5 = 5
5 + 5 = ten, but we're only using 0's and 5's, so that's 50
50 + 5 = 55
55 + 5 = 50 + (5 + 5) = 50 + 50 = one hundred, but no 1's so 500
500 + 5 = 505
505 + 5 = 550
550 + 5 = 555
555 + 5 = 5000...

In binary:
0 + 1 = 1
1 + 1 = 10
10 + 1 = 11
11 + 1 = 100
100 + 1 = 101
101 + 1 = 110
110 + 1 = 111
111 + 1 = 1000...

[Massageman]

A circuit (barring any quantum mechanics) is either "ON" or "OFF". Binary is the only understandable "system" which represents that change of status - "0" = off, "1" = on. Each is called a bit. Letters and numbers and made of a series of bits called a byte, words and commands are built from the letters and numbers.

[MysticDevice]

As far as I know the way it works is as follows. The old computers were build around lots and lots of individual pathways. The 1s and 0s indicate whether any particular pathway has power through it or not. "1" means power, "0" means no power.

And powering different combinations of pathways is what produces the information you see on the screen.

That's the extent of my knowledge and I'm sure its mostly wrong.

[slatyb]

What doesn't make sense? Have you looked at logic for a one bit adder? It takes three bits and produces a sum and a carry bit. Do you understand basic binary logic: and, or, and not?

[Siri137]

And, or and not are pretty straightforward, but why is three 00000011? Shouldn't it be 00000100? Because zero is 00000000, and one is 00000001, and two is 00000010.
It isn't logical at all, it makes zero (pun intended) sense.

[Sargentcaptain]

You're approaching this as if binary can only have 8 characters max, that's not the case for the binary system.
Computers will have a max number of characters they can use to store data, but that's a fundamental issue of data storage, not of the binary system.

And even if that was the case, that system of yours is very inefficient. How would you write 9, 17 and anything higher? The binary system can use 8 bits to show 256 different numbers (including 0). I don't see how your system would make sense for anything higher than 8.

If you've got a single bit to work with, it can be 1 or 0. If you've got 2, you get combos of 00, 01, 10, 11. In decimal, 0, 1, 2, 3. If you add another bit, you can get 000, 001, 010, 011, 100, 101, 110, 111.

Each bit will have a value of 2^bit. So in 101, the 1 on the right is 1^0 = 1. The 0 bit would be 2^1 = 2. The 1 on the left is 2^2 = 4. The more bits you have the larger your max number gets, and that increase is exponential, so it's very efficient at using a limited number of characters and character slots to write large numbers.

[strateguy632]

it works by switching the electricity on and off. are higher and lower, then the computer counts the pattern of 8 and translates it.

[NathanDavis]

I don't see the smiley in that pic... unless you mean the smile on that rolling skating bear...

[exitseven]

If you would like you can DM me with a more specific question and I will do my best to answer you. I teach Computer Science.

[LiamS95]

It's a binary language you have to understand binary math got it to make any sense.

[Siri137]

You don't say!

[LiamS95]

Lol
... yes

[KostasKouvalis]

Yeah, the equation that Isla posted, as a calculation is easy even for someone like me who struggles at math, but where I'm lost is, what that information actually means.

[IslaTheWitch]

@KostasKouvalis everything... anything you need to code :D and you need only 0 and 1 :D

servers DNS still work binary lol

[IslaTheWitch]

binary code represent numbers, letters, or other types of information... remember that every key on your keyboard has a numeric representation (i. e. enter = 13), almost everything is a number, an integer... so in binary code you can code the whole sequences of commands :D (computer god, forgive me this thinking shortcut)

[DrPepper12]

Base 1 number system like time is a base 60 number system ( thanks a lot Babylonians)!