"There is nothing better than effective coding, Amigo! Trust an old robot."
"Are you talking about ciphers used by spies?"
"Of course not. I'm talking about presenting information in a digestible form. About numeral systems. You are aware that in everyday life most people use the decimal system. It uses 10 symbols to represent every number: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. There are 10 numerals, so the system is called decimal."
"That was convenient for humans with their ten fingers. But programmers are big-time inventors. They immediately came up with encodings that use a different number of digits. For example, 2, 8, 16, or 64 digits. They did this to make it convenient for computers, which rely on 'there is a signal / there is no signal'."
"Ah, I see what they have in common... All these systems are based on powers of two.
"Good observation. Let's start with an encoding that involves 8 digits. Humans may find this the easiest: just drop the numbers 8 and 9 and — boom — you have the octal encoding (numeral system). You were recently told about literals, right?"
"Yes, I was."
"Well, surprise! You can set numeric literals encoded using the octal system. If, of course, you really need to. It's easier than it sounds. Just put 0 in front of the whole number.
"So if a numeric literal starts with zero, does that mean it's octal?"
"Yes, Java will treat it as octal.
|x is 13: 1*8+5|
|x is 21: 2*8+5|
|x is 83: 1*64+2*8+3 == 1*82+2*81+3*80|
|This will not compile: 8 is not one of the symbols used in the octal encoding.|
"It's unlikely that you need to write octal numbers in your code, but you should know what they are. "After all, you will have to read code written by others. And as mentioned above, programmers are big inventors.
Well, remember that you can't just go and write 0 in front of every number."
"But if I intend for it to be octal, then I can?"
"Even if you don't understand it yet, binary encoding is your native language. Let me remind you about it. If octal has only the digits 0-7, then binary has only 0 and 1."
"Why is this encoding necessary?"
"As I mentioned above, this has everything to do with the internal structure of a computer. Everything in a computer runs on electricity, and as it happens, the most efficient way to store and transmit something using electricity is to use two states: either there is no electricity in the wire (zero) and there is electricity (one)."
"That's why it is so popular... Hmm, it seems that I am indeed starting to remember this language!"
"All robots understand it perfectly. Although it is not used very often in Java. Java is considered a high-level language, completely abstracted from the hardware it runs on. Indeed, do you really care what format is used to store and process data inside a computer?
"But over the past decades, programmers have come to love the binary encoding (and other encodings based on it). As a result, Java has operators that take binary numbers as inputs. And the accuracy of floating-point numbers depends on their binary representation.
"In short, it is better for you to know about this encoding than to not know."
"Right. And as was the case with octal encoding, Java has a way to encode literals using the binary system."
"So they will only be made up of 0s and 1s?"
"Exactly. In order for the Java compiler to understand that the code contains a numeric literal encoded in binary rather than simply a decimal number consisting of zeros and ones, it is customary for all binary literals to begin with the prefix 0b (the 'b' comes from the word binary).
|х is 4: 1*4+0*2+0|
|х is 15: 1*8+1*4+1*2+1|
|х is 967: 1*29+1*28+1*27+1*26+0*25+0*24+0*23+1*22+1*2+1;|
|This will not compile: 2 is not one of the symbols used in the binary encoding.|
"What's two to the fourth power?"
"Sixteen. You figured out the right question to ask a robot that has come as far as me!"
"It seems to you that you have come far. Anyway, sixteen. In addition to octal and binary encodings, literals can also be written in hexadecimal. This is a very popular encoding.
"That is because although binary notation is as close as possible to how numbers are actually stored, it is too difficult for humans to effectively work with such numbers: in binary, the number one million 20 digits, not 7.
"That's why programmers came up with the hexadecimal system. After all, as you correctly noted, 16 is 2 raised to the 4th power, so exactly 4 bits correspond to one hexadecimal digit.
"So every 4 bits can now be written in a single hexadecimal digit."
"Right. The hexadecimal encoding also has its own unique prefix: 0x. Examples:
|Decimal number||Binary notation||Hexadecimal notation|
"Ok, so it's clear enough how we got the octal system: we just threw out the numbers 8 and 9. But where do we get the 6 missing digits for the hexadecimal system? I would like to see them!"
"It's all straightforward. The first 6 letters of the English alphabet were taken as the 6 missing digits: A (10), B (11), C (12), D (13), E (14), F (15).
|Hexadecimal notation||Binary notation||Decimal number|
"How do you convert a hexadecimal number to decimal?"
"It's very simple. Let's say you have the number 0xAFCF. How much is that in decimal? First, we have a positional number system, which means the contribution of each digit to the overall number increases by a factor of 16 as we move from right to left:
A*163 + F*162 + C*161 + F
The symbol A corresponds to the number 10, the letter C says we have the number 12, and the letter F represents fifteen. We get:
10*163 + 15*162 + 12*161 + 15
Raising 16 to the various powers that correspond to the digits, we get:
10*4096 + 15*256 + 12*16 + 15
We sum everything up and get:
"Now you know how 45007 is stored in memory."
"Yes, I do. It is 0xAFCF"
"Now let's convert it to binary. In binary it would be:
"Every set of four bits corresponds to exactly one hexadecimal character. That's super convenient. Without any multiplication or exponentiation."