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An integer overflow can cause the value to wrap and become negative, which violates the program's assumption and may lead to unexpected behavior (for example, 8-bit integer addition of 127 + 1 results in −128, a two's complement of 128).
An example, suppose we add 127 and 127 using 8-bit registers. 127+127 is 254, but using 8-bit arithmetic the result would be 1111 1110 binary, which is the two's complement encoding of −2, a negative number. A negative sum of positive operands (or vice versa) is an overflow.
The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the sum is 2 C + S {\displaystyle 2C+S} . The simplest half-adder design, pictured on the right, incorporates an XOR gate for S {\displaystyle S} and an AND gate for C {\displaystyle C} .
As an example, consider the signed 4-bit addition of 7 and 3: 0111 (carry) 0111 (7) + 0011 (3) ===== 1010 (−6) invalid! In this case, the far left two (MSB) carry bits are "01", which means there was a two's-complement addition overflow. That is, 1010 2 = 10 10 is outside the permitted range of −8 to 7. The result would be correct if ...
Saturation arithmetic also enables overflow of additions and multiplications to be detected consistently without an overflow bit or excessive computation, by simple comparison with the maximum or minimum value (provided the datum is not permitted to take on these values).
In addition and subtraction, the result may require one bit more than the operands. In multiplication of two unsigned integers with m and n bits, the result may have m+n bits. In case of overflow, the high-order bits are usually lost, as the un-scaled integer gets reduced modulo 2 n where n is the size of the storage area. The sign bit, in ...
Arithmetic and logical instructions set some or all of the flags, and conditional jump instructions take variable action based on the value of certain flags. For example, jz (Jump if Zero), jc (Jump if Carry), and jo (Jump if Overflow) depend on specific flags. Other conditional jumps test combinations of several flags.
Carry-out, which conveys the carry resulting from an addition operation, the borrow resulting from a subtraction operation, or the overflow bit resulting from a binary shift operation. Zero, which indicates all bits of Y are logic zero. Negative, which indicates the result of an arithmetic operation is negative.