nixCraft 🐧Jul 4, 2023
If you ever wanted a visual to explain how binary in works.
Show threadJason MadridJul 5, 2023

@nixCraft

I was literally today years old when I learned even this much about binary.

I was also today years old when it hit me that it goes by a "base 2" system (if my terminology is right, at least).

Meaning...
2 = 10
2^2 = 100
2^3 = 1000
2^4 = 10000
(And presumably 2^5 would have been 100000, if the gif had gone on any longer.)

Show threadZahmbieNDJul 5, 2023
@JMad17 @nixCraft Exactly! Binary is numbers in base 2, instead of our typical base 10 system. Computers use it because you can physically represent a digit with an "on" or "off" state of a transistor, switch, or wire. "on" or high voltage is usually 1, and "off" or low voltage is usually 0.
Other common base systems computer programmers use are hexadecimal (base 16), octal (base 8), and even base 64. That's because the power of 2 makes it easier to convert to/from binary.
Show threadZahmbieND
@JMad17 @nixCraft Example:
In hexadecimal, each digit is 0-15 (represented 0-9 and A-F), and the "tens place" is multiplied by 16, 2^4, which in binary is just adding 4 zeroes to the end, just enough room for the next digit.
0x41C3
3=binary 0011
C=12=binary 1100
1=binary 0001
4=binary 0100
0x41C3=binary 0100 0001 1100 0011
From binary to decimal:
2^14+2^8+2^7+2^6+2^1+2^0
=16384+256+128+64+2+1
=16835
From hex to decimal:
4×16^3+1×16^2+12×16^1+3×16^0
=4×4096+1×256+12×16+3×1
=16384+256+192+3
=16835
Jul 5, 2023 at 2:16pmWeb
Show threadZahmbieNDJul 5, 2023
@JMad17 @nixCraft Apologies, I had to edit this reply a couple of times. On some clients, * messes with formatting (hides the asterisk and italicizes the text between stars), so I changed my formulas to use × instead.