Formula to determine the range of signed and unsigned data types C++

Question

I\'m just starting out in C++ (literally my second day) and I\'ve been assigned to calculate the ranges of the varying data types, signed and unsigned. The problem is, the way m

Answer 1

In actuality, those ranges can be found in - see reference, and specifically the template std::numeric_limits - see here. I'm assuming though that you want to know where those numbers come from.

What matters is the number of bits. If you have n bits, then you can express 2ⁿ different values with them. Take an old-school 16-bit integer. With 16 bits, the amount of possible different values is 2¹⁶ = 65536. If you have an unsigned value, you're only expressing non-negative values. So the smallest value you express is 0, and the largest is 2ⁿ - 1, so a 16-bit unsigned integer goes from 0 to 65535.

If you are expressing integers with a sign, then of course you now have the same amount of values (65536 in the previous example) to express some positive and negative numbers. You've got 0 in the middle, and then you split the remaining values between negatives and positives. So you get -32768 on the low end and 32767 on the high end.

For any other datatype that represents an integer, it's the same pattern, whether it's 32, 64 or more bits.