Adding one to System.Int32.MaxValue

What would you expect to be displayed when you execute the following C# code:

int i = System.Int32.MaxValue;

i = i + 1;

Console.WriteLine("{0}", i);

What you end up getting is -2147483648. Let me explain why that is…

I’m not going to go into the ins and outs of how binary numbers work, as that is way beyond the scope of this blog post. A 32 bit number is represented by 32 1’s & 0’s. Each bit from right to left goes up in magnitude as to what it’s worth (much like the normal decimal based number system we are used to). So each bit is worth it’s value * (2^p) (where ^ means ‘to the power of’ and p is position of the bit). So the lsb (least significant bit) is worth it’s value * 2^0. Anything to the power of 0 is one so the lsb is worth 0 or 1 (or 0*1 or 1*1). The next significant bit is worth it’s value * 2^1 so 0 or 2. This process carries on for each of the first 31 bits.

Now due to the fact an Int32 is a signed integer (we can represent negative numbers) the msb (most significant bit) doesn’t represent it’s value * 2^31 (31 not 32 as we start counting at 0) but instead it represents it’s value * – (2^31). So effectively either 0 or -2147483648.

If we think about the actual binary representation of System.Int32.MaxValue it is 0111 1111 1111 1111 1111 1111 1111 1111 (note I’ve added spaces to make it easier to read), well when you add one to that value it becomes 1000 0000 0000 0000 0000 0000 0000 0000 or -2147483648. A more in depth summary of how binary counting works is available on Wikipedia.

As an aside -1 is represented by 32 1’s (1111 1111 1111 1111 1111 1111 1111 1111). So when you add 1 to -1 you end up with 32 0’s which is 0. Representing binary numbers in this way is known as two’s complement. It is done like this as it means you can logically add numbers for addition and subtraction (for subtraction simply turn a number negative and add it). Wikipedia has a very informative article on two’s comlement if you’re interested in reading more.