You could do a short on how to count binary on your fingers ;)

​@LeftandRight A computer speaks in binary. Understanding how base 2 numbers work is necessary to understand programming stuff, e.g. file sizes (Why is a KiB equal to 1024 bytes? Because 1024 is 2 to the power of ten) or bitwise operators that are more frequently used in low level programming languages (C or C++ for example). It's also needed to understand how numbers are stored in a computer and how a CPU does arithmetic operations on base 2 numbers. It's part of every computer science curriculum. Another interesting thing about this is once you understand how bases work, you can count in any base. The third most common base is 16 and the format is called hexadecimal. Since numbers end with 9, hexadecimal uses letters as well.

Nope, it was at school :) but things like this easy to forget, so thank you, that was refreshing.)

Nope... 30 years ago.. while programming Z80 assembly 😁

I learned about different numbering systems in primary school, in the UK, over 50 years ago. Is this a US thing, or a sad indictment of modern teaching?

Don't blame us man! Some of us never had a chance to even see computers while we learnt about computers!

Thanks for the kind words :)

You're welcome, thanks for the kind words.

You can definitely truncate unused zeroes from the left when representing a single number. The number I wrote was 8 bits that would fit into 1 byte on a computer. The representation is necessary so a computer knows where the binary number starts and ends. For larger numbers, keep adding digits on the left.

If I'm not mistaken, in programming, those 8 bits are a "byte". Once you go over a byte (128), you start adding bytes together. In just using binary (not programming), then yes, I think you would just keep adding digits on the left. Depends on the context. (I'm sure others will correct me if I'm wrong).

@@cwlindWX A byte is 0-255

It's all about powers of 2.... Use the same substraction method he used. Say your number is 16,000. The binary representation is: 0011111010000000. You can see bits 8192,4096,2048,1024,512,128 are 'flipped'. The decimal values under binary won't show up well but it looks like this: 32768,16384,8192,4096,2048,1024,512,256,128,64,32,16,8,4,2,1

@@ZacKoch thanksss!!! What does flip mean?

@@marouk10 0 not flipped or off, 1 flipped or on

@@ZacKoch ohhhh righttt okok thanksss

you can just cut off the 00 at front, they hold no value so not needed to place them

I'd love to hear a clear bit-shifting / bit-masking explanation, that'd be very useful. I've had someone try to explain it and they just made it more confusing than it really is. Had to learn it on my own.

@@scruffygaming627 It's sometimes best to think about bit shifting in the context of base 10 multiplication. For instance, you have a number 10.1 multiply it by 10 to get the number 101. What happened to the decimal ? It "shifted" right one decimal place. To get more complicated, think about a memory register such as 0000 0101. If you shift to the right, the value becomes 0000 0010, but if you shift back to the left, you get 0000 0100. Which is an example of how / why one needs to be careful. In the case of a memory register this could likely be very important. But Coordinate math in a game likely not important at all. There is a book out there I read in the (90's ? ) By a guy named Andre Lamothe I believe, called tips and tricks of the game programming gurus. He has a very good explanation of bit shifting. Now as for bit masking, well you need to fully understand AND/OR operations, and perhaps learn about memory registers. Bit masking for me hit home once I started learning about embedded hardware, and bit shifting hit home when when I was learning graphics programming for mode 13h(very old school). I'd consider the two related. One last thing. You're going to need to convert between Base 10Base 16Base 2 alot while learning. Which is why I suggested Microsofts Calculator in programmers mode. I'm sure there is a equivalent in other operating systems as well. But personally I always write my code from Windows, and mostly compile on Linux. As I'm usually cross compiling for ARM.

I should also point out. That bit operations wont work with floating point numbers. You need to understand the specification as to why. But you need to use integer type numbers for bit operations to work. There is a way around that though. Known as fixed point math. But worry about that later . . .

Sometimes i wonder if technology would be more advanced if computers were not restricted to human thinking. :) Look at how a machines write code compared to humans. Computers are far more efficient thinkers/doers. One of the reasons AI development will surprise human.

@@scruffygaming627 agrees but not my original point. Decimal is the default in the human mind due to historical reasons. Kinda arbitrary. Hex or Oct-based system is more natural.