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In the first case, because you're dealing with a number, the compiler does numerical addition, and stores the sum as a new number. myNumberPlusOne is therefore stored as 0000 0000 0000 0001 0000 0000 0000 0000, which is a value one bigger than myNumber. Total size: still 4 bytes.

In the first case, because you're dealing with a number, the compiler does numerical addition, and stores the sum (65535 + 1 = 65536) as a new number. myNumberPlusOne is therefore stored as 0000 0000 0000 0001 0000 0000 0000 0000, which is a value one bigger than myNumber. Total size: still 4 bytes.

Data has a type. For example, this answer is a text type, known to developers as a string. A number is a different type. There are several number types, based on what it is you're storing (int for integers, uint for positive integers, long for bigger integers, float or double for decimal values, ...).

Here, you can see why data types matter. We store things differently, and we also treat that data differently. Why? Because it makes sense to us that + on numbers means numerical addition, whereas + on strings means string concatenation (= appending).

TL;DR
The key takeaway here is that there is a world of difference between the number 65535 and a piece of text which represents the digits '6', '5', '5', '3' and '5'. It may look the same to you when rendered on a computer screen, but to a computer internally, they are completely unrelated to one another.

The rest of this answer is a lengthy elaboration on what that means and how it is used in everyday computing.

Data has a type. For example, this answer is a text type, known to developers as a string. A number is a different type. There are several number types, based on what it is you're storing (int for integers, uint for positive integers, long for bigger integers, float or double for decimal values, ...).

Cool trick:
Take a Microsoft Office file (.docx or .xlsx, not the older versions), change its file extension to .zip, and open it. Lo and behold, this is a perfectly working zip archive! Since the advent of the .docx (instead of .doc) and .xlsx (instead of .xls) filetypes, Office has really been storing all of its data using ZIP archiving methods.

Here, you can see why data types matter. We store things differently, and we also treat that data differently. Why? Because it makes sense to us that + on numbers means numerical addition, whereas + on strings means string concatenation (= appending).

To summarize, the key takeaway here is that there is a world of difference between the number 65535 and a piece of text which represents the digits '6', '5', '5', '3' and '5'. It may look the same to you when rendered on a computer screen, but to a computer internally, they are completely unrelated to one another.

Or, alternatively, I could store my students' pass/fail on an exam using a simply stream of bits where 1 is pass and 0 is fail, and I know the order of my students based on some other data I've stored somewhere else. This is a highly efficient storage mechanism in terms of data size, but it is also very inflexible in terms of storing additional information (e.g. absentees).

Here's an online converter so you can play around with this (you can press "Swap" to switch converting to or from binary.

Or, alternatively, I could store my students' pass/fail on an exam using a simple stream of bits where 1 is pass and 0 is fail, and I know the order of my students based on some other data I've stored somewhere else (not in this file). This is a highly efficient storage mechanism in terms of data size, but it is also very inflexible in terms of storing additional information (e.g. absentees).

Here's an online converter so you can play around with this (you can press "Swap" to switch converting to or from binary).

In programming terms, your variable type matters, because it indicates to the compiler how your data should be stored, and how it should be handled.

int myNumber = 65535;
string myString = "65535";

In the first case, it will store your value numerically. 65535 (decimal) is 1111 1111 1111 1111 in binary. However, int is always 4 bytes, so it gets stored as 0000 0000 0000 0000 1111 1111 1111 1111. Total size: 4 bytes.

In the second case, it will store each individual text character, which we already know from before is 0011 0110 0011 0101 0011 0101 0011 0011 0011 0101. Total size: 5 bytes.

Now here's an interesting curve ball:

int myNumberPlusOne = myNumber + 1;
string myStringPlusOne = myString + 1;

In the first case, because you're dealing with a number, the compiler does numerical addition, and stores the sum as a new number. myNumberPlusOne is therefore stored as 0000 0000 0000 0001 0000 0000 0000 0000, which is a value one bigger than myNumber. Total size: still 4 bytes.

In the second case, because you're dealing with text, the compiler appends the 1 to the text. Now, you're storing a 6-character string, 655351, which in binary is 0011 0110 0011 0101 0011 0101 0011 0011 0011 0101 0011 0001. Total size: 6 bytes.

Here, you can see why data types matter. We store things differently, and we also treat that data differently. Why? Because it makes sense to us that + on numbers means numerical addition, whereas + on strings means string concatenation (= appending).