Overflow flag
Encyclopedia
In computer
processor
s, the overflow flag (sometimes called V flag) is usually a single bit
in a system status register
used to indicate when an arithmetic overflow
has occurred in an operation, indicating that the signed two's-complement result would not fit in the number of bits used for the operation (the ALU width). Some architectures may be configured to automatically generate an exception
on an operation resulting in overflow.
Although not very precise, the overflow flag could be considered a two's complement
form of a carry flag
, but the typical usage is quite different.
An illustrative example is what happens if we add 127 and 127 using 8-bit registers. 127+127 is 254, but using 8-bit aritmetics the result would be 1111 1110 binary, which is -2 in two's complement
, and thus negative. A negative result out of positive operands (or vice versa) is an overflow. The overflow flag would then be set so the program can be aware of the problem and mitigate this or signal an error. The overflow flag is thus set when the most significant bit (here considered the sign bit) is changed by adding two numbers with the same sign (or subtracting two numbers with opposite signs). Overflow never occurs when the sign of two addition operands are different (or the sign of two subtraction operands are the same).
Internally, the overflow flag is usually generated by an exclusive or of the internal carry into and out of the sign bit. As the sign bit is the same as the most significant bit of a number considered unsigned, the overflow flag is "meaningless" and normally ignored when unsigned numbers are added or subtracted.
The overflow flag is typically changed by all arithmetic operations, including compare instructions (equivalent to a subtract instruction without storing the result). In many processor architectures, the overflow flag is cleared by bitwise operations (and, or, xor, not), possibly including shifts and rotates, but it may also be left undefined by these. Instructions such as multiply and divide often leave the flag undefined, or affected by the last partial result.
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
processor
Central processing unit
The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...
s, the overflow flag (sometimes called V flag) is usually a single bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
in a system status register
Status register
A status register or flag register is a collection of flag bits for a processor. An example is the FLAGS register of the x86 architecture....
used to indicate when an arithmetic overflow
Arithmetic overflow
The term arithmetic overflow or simply overflow has the following meanings.# In a computer, the condition that occurs when a calculation produces a result that is greater in magnitude than that which a given register or storage location can store or represent.# In a computer, the amount by which a...
has occurred in an operation, indicating that the signed two's-complement result would not fit in the number of bits used for the operation (the ALU width). Some architectures may be configured to automatically generate an exception
Exception handling
Exception handling is a programming language construct or computer hardware mechanism designed to handle the occurrence of exceptions, special conditions that change the normal flow of program execution....
on an operation resulting in overflow.
Although not very precise, the overflow flag could be considered a two's complement
Two's complement
The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two...
form of a carry flag
Carry flag
In computer processors the carry flag is a single bit in a system status register used to indicate when an arithmetic carry or borrow has been generated out of the most significant ALU bit position...
, but the typical usage is quite different.
An illustrative example is what happens if we add 127 and 127 using 8-bit registers. 127+127 is 254, but using 8-bit aritmetics the result would be 1111 1110 binary, which is -2 in two's complement
Two's complement
The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two...
, and thus negative. A negative result out of positive operands (or vice versa) is an overflow. The overflow flag would then be set so the program can be aware of the problem and mitigate this or signal an error. The overflow flag is thus set when the most significant bit (here considered the sign bit) is changed by adding two numbers with the same sign (or subtracting two numbers with opposite signs). Overflow never occurs when the sign of two addition operands are different (or the sign of two subtraction operands are the same).
Internally, the overflow flag is usually generated by an exclusive or of the internal carry into and out of the sign bit. As the sign bit is the same as the most significant bit of a number considered unsigned, the overflow flag is "meaningless" and normally ignored when unsigned numbers are added or subtracted.
The overflow flag is typically changed by all arithmetic operations, including compare instructions (equivalent to a subtract instruction without storing the result). In many processor architectures, the overflow flag is cleared by bitwise operations (and, or, xor, not), possibly including shifts and rotates, but it may also be left undefined by these. Instructions such as multiply and divide often leave the flag undefined, or affected by the last partial result.