What actually happens when a Byte overflows?

Question

What actually happens when a Byte overflows?

Say we have

byte byte1 = 150; // 10010110  
byte byte2 = 199; // 11000111

If we now do this addition

byte byte3 = byte1 + byte2;

I think we'll end up with byte3 = 94 but what actually happens? Did I overwrite some other memory somehow or is this totally harmless?

Answer 1

It's quite simple. It just does the addition and comes off at a number with more than 8 bits. The ninth bit (being one) just 'falls off' and you are left with the remaining 8 bits which form the number 94.

(yes it's harmless)

Answer 2

In C# if you have

 checked { byte byte3 = byte1 + byte2; }

It will throw an overflow exception. Code is compiled unchecked by default. As the other answers are saying, the value will 'wrap around'. ie, byte3 = (byte1 + byte2) & 0xFF;

Answer 3

The top bits will be truncated. It is not harmful to any other memory, it is only harmful in terms of unintended results.

Answer 4

The carry flag gets set... but besides the result not being what you expect, there should be no ill effects.

Answer 5

Typically (and the exact behaviour will depend on the language and platform), the result will be taken modulo-256. i.e. 150+199 = 349. 349 mod 256 = 93.

This shouldn't affect any other storage.

Answer 6

Since you have tagged your question C#, C++ and C, I'll answer about C and C++. In c++ overflow on signed types, including sbyte (which, I believe, is signed char in C/C++) results in undefined behavior. However for unsigned types, such as byte (which is unsigned char in C++) the result is takes modulo 2ⁿ where n is the number of bits in the unsigned type. In C# the second rule holds, and the signed types generate an exception if they are in checked block. I may be wrong in the C# part.

Answer 7

Overflow is harmless in c# - you won't overflow memory - you simply obly get the last 8 bits of the result. If you want this to this an exception, use the 'checked' keyword. Note also that you may find byte+byte gives int, so you may need to cast back to byte.

Answer 8

The behavior depends on the language.

In C and C++, signed overflow is undefined and unsigned overflow has the behavior you mentioned (although there is no byte type).

In C#, you can use the checked keyword to explicitly say you want to receive an exception if there is overflow and the unchecked keyword to explicitly say you want to ignore it.

Answer 9

Leading bit just dropped off.

Answer 10

And arithmetic overflow occurs. Since 150+199=349, binary 1 0101 1101, the upper 1 bit is dropped and the byte becomes 0101 1101; i.e. the number of bits a byte can hold overflowed.

No damage was done - e.g. the memory didn't overflow to another location.

Answer 11

Let's look at what actually happens (in C (assuming you've got the appropriate datatype, as some have pointed out that C doesn't have a "byte" datatype; nonetheless, there are 8-bit datatypes which can be added)). If these bytes are declared on the stack, they exist in main memory; at some point, the bytes will get copied to the processor for operation (I'm skipping over several important steps, such as processsor cacheing...). Once in the processor, they will be stored in registers; the processor will execute an add operation upon those two registers to add the data together. Here's where the cause of confusion occurs. The CPU will perform the add operation in the native (or sometimes, specified) datatype. Let's say the native type of the CPU is a 32-bit word (and that that datatype is what is used for the add operation); that means these bytes will be stored in 32-bit words with the upper 24 bits unset; the add operation will indeed do the overflow in the target 32-bit word. But (and here's the important bit) when the data is copied back from the register to the stack, only the lowest 8 bits (the byte) will be copied back to the target variable's location on the stack. (Note that there's some complexity involved with byte packing and the stack here as well.)

So, here's the upshot; the add causes an overflow (depending on the specific processor instruction chosen); the data, however, is copied out of the processor into a datatype of the appropriate size, so the overflow is unseen (and harmless, assuming a properly written compiler).

Answer 12

As far as C# goes, adding two values of type byte together results in a value of type int which must then be cast back to byte.

Therefore your code sample will result in a compiler error without a cast back to byte as in the following.

byte byte1 = 150; // 10010110  
byte byte2 = 199; // 11000111

byte byte3 = (byte)(byte1 + byte2);

See MSDN for more details on this. Also, see the C# language specification, section 7.3.6 Numeric promotions.