How to know if it is either a positive/negative number or it is referring to a number in binary?

Question

I'm learning Integer data formats in a computer science book and as far as I understand that binary representation of a integer whether it is positive or negative is to have the leftmost bit (msb) be either a 0 for positive or 1 for negative, lets say in a 8-bit computer how would I know if it is talking about 10000010 - 130 in base 10 or if it is referring to negative 2? I might be wrong, if i'm please correct me.

Answer 1

If you were to just see the string 10000010 somewhere, I don't know... written on a wall or something, how would you know how to interpret it?

You might say, hey, that's ten million and ten ( you thought it was base 10 ) or you might say hey, that's -126 ( you thought it was two's complement binary ), or you might say that's positive 130 ( you thought it was standard binary ).

It is, in a theoretical sense, up to whatever is doing the interpreting how it is interpreted.

So, when a computer is holding 8 bits of data, it's up to it how it interprets it.

Now if you're programming, you can tell the computer how you want something interpreted. For example, in c++

// char is 1 byte
unsigned char x = 130u;

Here I have told the compiler to put 130 unsigned into a byte, so the computer will store 10000010 and will interpret it as the value 130

Now consider

// char is 1 byte
char x = -126;

Here I have told the compiler to put -126 signed into a byte, so the computer will again store 10000010 but this time it will interpret it as the value -126.

Answer 2

Take a look at the answer posted to this question: Negative numbers are stored as 2's complement in memory, how does the CPU know if it's negative or positive?

The CPU uses something called an opcode in order to determine which function it will take when manipulating a memory location (in this case, the value 10000010). It is that function within the CPU that will either manipulate it as a negative or a positive number. The CPU doesn't have access to whether or not the number is signed or unsigned - it uses the op code when manipulating that number to determine whether or not it should be a signed or unsigned operation.