In binary addition, overflow occurs when the sum of two binary numbers exceeds the maximum representable value. This happens because binary numbers have a specific range of representable values based on the number of they contain. When the sum exceeds this range, the result cannot be accurately represented, resulting in an . For example, in a simple 4-bit binary addition, 1101 + 0101, the sum is 10010. However, since we are working with only a 4-bit register, the most significant bit (MSB) of the sum cannot be represented, resulting in overflow, so we discard the MSB, giving an answer of 0010.
The consequences of binary overflow can be severe, leading to incorrect computation results where the result may wrap around or be truncated, causing calculations. In signed representations, overflow can cause a positive number to become negative and vice versa, resulting in sign errors. Some systems or programming languages detect overflow and raise exceptions, which may crash programs, posing security vulnerabilities that can lead to buffer overflows and data .
On the other hand, binary underflow occurs when subtraction is performed on binary numbers, and the result is smaller than the minimum representable value. Just like overflow, underflow happens because binary numbers have on the representable values based on the number of bits used. For instance, in a 5-bit binary subtraction of 01010 - 10101, the result yields -10011, which cannot be accurately represented in 5 bits, causing underflow. In such cases, the correct result would involve using additional bits or a different representation to accurately represent the value.
The consequences of binary underflow include rounding to zero if the result is smaller than the smallest representable value, leading to a loss of significant digits or precision. Some systems treat underflow as an error, causing exceptions or if not handled properly.
