As the others have said binary is a number system based on 2. It’s the basis of all computing and I’ve done a lot of work with binary in my early career.
When programming I have also used octal (base 8) and hexadecimal (base 16). In hexadecimal the numbers go 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10. So 10 in hexadecimal (often shortened to hex) is 16 in decimal, 1A in hex is 26 in decimal and FF in hex is 255 in decimal.
Binary code is a way of counting, instead of counting from 0 to 10 you count from 0 to 1. E.g. two in decimal is 2, in binary is 1 + 1 => 10 (one-zero).
This way of counting has been invented as it comes useful when you have transistors or electronics as those things can have only to state: on (1) and off (0).
Binary is very important both for computer scientists and for electronic engineers, because a lot of operations which are performed at “low level” (i.e. they reconfigure the hardware) have to be performed having in mind that things can either be on or off.
As extension of binary there is the hexadecimal, which is a different way of counting from 0 to 15 (you go 0, 1, 2…, 9, 10, A, B, C…F). We use 16 values because 16 is exactly the maximum number you can fit in a byte (8 bits, up to 8 times 1). This is something that electronic engineers and computer scientists need to master as well.
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