Min and Max value of integral type in C#

Question

Whats the mathematical formulae to calculate the MIN and MAX value of an integral type using your calculator. I know you can use Integer.Max or Integer.Min etc or look it up on msdn however I want to know how to calculate it.

Answer 1

For unsigned types:

• Min value = 0
• Max value = (2 ** (number of bits)) - 1

So, for UInt32:

Min value = 0

Max value = (2 ** 32) - 1
          = 4294967296 - 1
          = 4294967295

For signed types:

• Min value = 0 - (2 ** (number of bits - 1))
• Max value = (2 ** (number of bits - 1)) - 1

So, for Int32:

Min value = 0 - (2 ** (32 - 1))
          = 0 - (2 ** 31)
          = 0 - 2147483648
          = -2147483648

Max value = (2 ** (32 - 1)) - 1
          = (2 ** 31) - 1
          = 2147483648 - 1
          = 2147483647

Answer 2

I'm using a 32bits signed integer in this example. 31 bits are used for the value creating 2^31 possibilities. As zero has to be included, you have to subtract one.

2^31-1

When negative, zero doesn't have to be included, thus you get the full range.

-2^31

In case of a unsigned integer, the max is simply 2^32-1, and the min 0.

Answer 3

You need to know how many bits the type is and whether it is signed or not.

For example, an int is 32-bits in C# and is signed. This means there are 31 bits to represent the number (1 bit is used to determine negative or postive). So you would calculate 2³¹ and subtract one which is 2147483647, (which is what Integer.MaxValue returns).

Similary a byte is 8 bits and not signed so the max value is 2⁸ -1 or 255.

Answer 4

An example for your question answer

int signed:

Min=(1 << ((sizeof(int) * 8) - 1));
Max=~(1 << ((sizeof(int) * 8) - 1));

also

Min=~(int)((~((uint)0))>>1);
Max=(int)((~((uint)0))>>1);

int unsigned:

Min=0;
Max=~((uint)0);

Answer 5

The Min/Max value of an Integer variable is derived from the amount of bits used (usually to the power of 2, ie 2bits, 4bits, 8bits). An INT in C# uses 32 bits, and as such can have a MAX value of 4,294,967,295 - as this is the maximum value 32 bits of data can represent - as is my understanding, anyway.

Answer 6

http://en.wikipedia.org/wiki/Integer_%28computer_science%29

Answer 7

If your calculator has a decimal-to-binary conversion (dec-to-hex would also work), try converting Int32.MaxValue and see if you spot the pattern ...

Answer 8

I believe you'll find this helpful:
Integer (Computer Science) @ Wikipedia