byte + byte = int… why?

Looking at this C# code:

byte x = 1;
byte y = 2;
byte z = x + y; // ERROR: Cannot implicitly convert type 'int' to 'byte'

The result of any math performed on byte (or short) types is implicitly cast back to an integer. The solution is to explicitly cast the result back to a byte:

byte z = (byte)(x + y); // this works

What I am wondering is why? Is it architectural? Philosophical?

We have:

• int + int = int
• long + long = long
• float + float = float
• double + double = double

So why not:

• byte + byte = byte
• short + short = short?

A bit of background: I am performing a long list of calculations on “small numbers” (i.e. < 8) and storing the intermediate results in a large array. Using a byte array (instead of an int array) is faster (because of cache hits). But the extensive byte-casts spread through the code make it that much more unreadable.