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The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...
Overflow cannot occur when the sign of two addition operands are different (or the sign of two subtraction operands are the same). [1] When binary values are interpreted as unsigned numbers, the overflow flag is meaningless and normally ignored. One of the advantages of two's complement arithmetic is that the addition and subtraction operations ...
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.
The Network Time Protocol has an overflow issue related to the Year 2038 problem, which manifests itself at 06:28:16 UTC on 7 February 2036, rather than 2038. The 64-bit timestamps used by NTP consist of a 32-bit part for seconds and a 32-bit part for fractional second, giving NTP a time scale that rolls over every 2 32 seconds (136 years) and ...
Such overflow bugs may be hard to discover and diagnose because they may manifest themselves only for very large input data sets, which are less likely to be used in validation tests. [51] The Year 2000 problem was a series of bugs where overflow errors occurred due to use of a 2-digit format for years.
Starting with Ruby version 1.9.2 (released on 18 August 2010), the bug with year 2038 is fixed, [16] by storing time in a signed 64-bit integer on systems with 32-bit time_t. [17] Starting with NetBSD version 6.0 (released in October 2012), the NetBSD operating system uses a 64-bit time_t for both 32-bit and 64-bit architectures.
For example, adjusting the volume level of a sound signal can result in overflow, and saturation causes significantly less distortion to the sound than wrap-around. In the words of researchers G. A. Constantinides et al.: [1] When adding two numbers using two's complement representation, overflow results in a "wrap-around" phenomenon.
Arbitrary-precision arithmetic can also be used to avoid overflow, which is an inherent limitation of fixed-precision arithmetic. Similar to an automobile's odometer display which may change from 99999 to 00000, a fixed-precision integer may exhibit wraparound if numbers grow too large to represent at the fixed level of precision.