6.2 Integer Arithmetic

Each of the basic arithmetic operations in C has two variants for integers: signed and unsigned. The choice is determined by the data types of their operands.

Each integer data type in C is either signed or unsigned. A signed type can hold a range of positive and negative numbers, with zero near the middle of the range. An unsigned type can hold only nonnegative numbers; its range starts with zero and runs upward.

The most basic integer types are int, which normally can hold numbers from -2,147,483,648 to 2,147,483,647, and unsigned int, which normally can hold numbers from 0 to 4,294.967,295. (This assumes int is 32 bits wide, always true for GNU C on real computers but not always on embedded controllers.) See Integer Types, for full information about integer types.

When a basic arithmetic operation is given two signed operands, it does signed arithmetic. Given two unsigned operands, it does unsigned arithmetic.

If one operand is unsigned int and the other is int, the operator treats them both as unsigned. More generally, the common type of the operands determines whether the operation is signed or not. See Common Type.

Printing the results of unsigned arithmetic with printf using ‘%d’ can produce surprising results for values far away from zero. Even though the rules above say that the computation was done with unsigned arithmetic, the printed result may appear to be signed!

The explanation is that the bit pattern resulting from addition, subtraction or multiplication is actually the same for signed and unsigned operations. The difference is only in the data type of the result, which affects the interpretation of the result bit pattern, and whether the arithmetic operation can overflow (see the next section).

But ‘%d’ doesn’t know its argument’s data type. It sees only the value’s bit pattern, and it is defined to interpret that as signed int. To print it as unsigned requires using ‘%u’ instead of ‘%d’. See The GNU C Library in The GNU C Library Reference Manual.

Arithmetic in C never operates directly on narrow integer types (those with fewer bits than int; Narrow Integers). Instead it “promotes” them to int. See Operand Promotions.