Display theory, bit, byte, binary shift and other (ENG)

Bit - (8, 16, 24, 32....) the minimum amount of information represented in the binary system. 1 or 0 symbolizes the status (on/off)

The game presents an example of one bit and it is a switch for electrical networks

Bytes are containers that store information from 1/0

8 bit = 1 byte

And to demonstrate the bit shift, I will use a 32-bit circuit
Below is a part of it, with white color indicating a byte and copper color indicating a bit

To confirm, here is the site[convertlive.com]

How to get 13 in 1101? ¯\_(ツ)_/¯

To convert ordinary 13 to binary, use the division operation with the remainder

Thus, the binary representation of 13 is 1101

When converting a decimal number to binary, you use the method of division by 2. If the number is divisible by 2, you write 0 (there is no remainder), and if the number is not divisible by 2, you write 1 (because we get the remainder). This rule is applied at each step of dividing a decimal number by 2 until the result is 0. After that, the remainders are written in reverse order to get the binary representation of the number.

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An example based on game logic

Next, we'll use the online calculator, and this section is designed to help you understand the magic it creates

Sign bit. The leftmost bit in the number indicates the sign for a decimal number

For a 4-bit 1010, the most significant bit will be 1010, and for an 8-bit 1011 1011, respectively 1011 1011

For example, if I take 1 and shift it by 31, we will get the maximum negative value for 32-bit programs -2147483648

In the photo, none of the indicators are on, because the value is negative

However, if there is a 30-bit offset, the value will be 1073741824

Example of the MSB on a calculator

A Factorio is written in 32 bits

So, the representation of the maximum and minimum values for this bit depth is as follows

MIN -2 147 483 648 MAX 2 147 483 647

Feature:

If you add one to the maximum value, you get the minimum value

2 147 483 647

+1

-2 147 483 648

Similar to the minimum value

-2 147 483 648

-1

2 147 483 647

An overflow occurs when the result of an arithmetic operation goes beyond the possible range for a particular number format.
For example, in the binary representation of 32-bit numbers, if you add one to the maximum value, an overflow occurs, and the minimum value is obtained.

An example of overflow in life is the "tachometer"
When the maximum is reached, a new cycle begins

If you create a number of items close to the maximum value for 32 bits. The game may start to slow down and crash when it is overcrowded.
I can't give you a live example of this because I don't want to wait that long (>__<)

Bit shift is the movement of bits in a binary number to the left or right. When a bit goes outside the number, it is lost, and new bits fill the empty spaces

I'll use a visual demonstration.
Let's take 13, which usually looks like this
Here, the bit shift is 1

Now let's shift left by 5

Moving by 5, we have 416 instead of 13
Although 1101 is also suitable for 13, 416 is simply found in a different place in the byte

By performing a bit shift, we ended up changing the decimal value on the output.

How it works in the game

https://youtu.be/fHAFPdr4fiU?si=L1X35fRtSTcCs2wt

In the constant combinator, data/values are set, then they get into the combinator that controls the bit shift: by the values 1,2,3..... and the direction to the right (>>) or left (<<)

Next, the signal goes to the arithmetic combinators, which in our case together play the role of 1 byte or 8 bits

From them, the signal goes to the combinator that divides by the remainder (%) *number* % 2

Take a display from the guide

https://steamcommunity.com/sharedfiles/filedetails/?id=3168628437

I will show you with the following example
Where 1 is a decimal representation and 2 is a bit representation

I take our symbol A into the combinator and shift it by 1
And we got a value with a plus sign.
Let me remind you that the condition for the display lamps to light up is the following "symbol" < 0

However, if you shift it by 2, the value will be minus because segment A should be lit on a two

The decimal value of a "symbol" is a bit code. It contains information about when the signal is positive and when it is negative. That is, thanks to it, small lamps know when they need to work and when not

Here is a 32-bit schematic and several ready-made display options

Install the "Text Plates"[mods.factorio.com] mod to see the characters

https://factoriobin.com/post/8iUNMTDm

Bit numbering
https://hmn.wiki/uk/Most_significant_bit

Bit
https://en.wikipedia.org/wiki/Bit

Sign bit
https://en.wikipedia.org/wiki/Sign_bit

Bit to byte
https://citizenmaths.com/ru/data-storage/32-bit-to-byte

Overflow
https://en.wikipedia.org/wiki/Integer_overflow

Bit shift
https://www.wikiwand.com/en/Bitwise_operation

https://www.wikiwand.com/uk/%D0%91%D1%96%D1%82%D0%BE%D0%B2%D0%B8%D0%B9_%D0%B7%D1%81%D1%83%D0%B2

Division with remainder
https://www.wikiwand.com/en/Euclidean_division

Factorio wiki
https://wiki.factorio.com/Arithmetic_combinator/uk

Most significant bit (MSB)
https://www.techtarget.com/whatis/definition/most-significant-bit-or-byte
https://youtu.be/KReHvV2SQj0?si=3UE24uqHKK_ONdYG

Scheme concept
https://youtu.be/KTdvGZfWMX4?si=iMD7NGpLYN9P_XW_