Sign extension (abbreviated as sext) is the operation, in
computer arithmetic
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numb ...
, of increasing the number of
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s of a
binary number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one).
The base-2 numeral system is a positional notatio ...
while preserving the number's
sign (positive/negative) and value. This is done by appending digits to the
most significant side of the number, following a procedure dependent on the particular
signed number representation
In computing, signed number representations are required to encode negative numbers in binary number systems.
In mathematics, negative numbers in any base are represented by prefixing them with a minus sign ("−"). However, in RAM or CPU regist ...
used.
For example, if six bits are used to represent the number "
00 1010" (decimal positive 10) and the sign extend operation increases the
word length
In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word (the ''word si ...
to 16 bits, then the new representation is simply "
0000 0000 0000 1010". Thus, both the value and the fact that the value was positive are maintained.
If ten bits are used to represent the value "
11 1111 0001" (decimal negative 15) using
two's complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian ...
, and this is sign extended to 16 bits, the new representation is "
1111 1111 1111 0001". Thus, by padding the left side with ones, the negative sign and the value of the original number are maintained.
In the
Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 seri ...
x86 instruction set
The x86 instruction set refers to the set of instructions that x86-compatible microprocessors support. The instructions are usually part of an executable program, often stored as a computer file and executed on the processor.
The x86 instruction ...
, for example, there are two ways of doing sign extension:
* using the instructions
cbw,
cwd,
cwde, and
cdq: convert byte to word, word to doubleword, word to extended doubleword, and doubleword to quadword, respectively (in the x86 context a byte has 8 bits, a word 16 bits, a doubleword and extended doubleword 32 bits, and a quadword 64 bits);
* using one of the sign extended moves, accomplished by the
movsx ("move with sign extension") family of instructions.
Zero extension
A similar concept is zero extension (abbreviated as zext). In a move or convert operation, zero extension refers to setting the high bits of the destination to zero, rather than setting them to a copy of the most significant bit of the source. If the source of the operation is an unsigned number, then zero extension is usually the correct way to move it to a larger field while preserving its numeric value, while sign extension is correct for signed numbers.
In the x86 and x64 instruction sets, the
movzx instruction ("move with zero extension") performs this function. For example,
movzx ebx, al copies a byte from the
al register to the low-order byte of
ebx and then fills the remaining bytes of
ebx with zeroes.
On x64, most instructions that write to the entirety of lower 32 bits of any of the general-purpose registers will zero the upper half of the destination register. For example, the instruction
mov eax, 1234 will clear the upper 32 bits of the
rax register....
See also
*
Arithmetic shift
In computer programming, an arithmetic shift is a shift operator, sometimes termed a signed shift (though it is not restricted to signed operands). The two basic types are the arithmetic left shift and the arithmetic right shift. For binary ...
and
logical shift
In computer science, a logical shift is a bitwise operation that shifts all the bits of its operand. The two base variants are the logical left shift and the logical right shift. This is further modulated by the number of bit positions a gi ...
References
* Mano, Morris M.; Kime, Charles R. (2004). ''Logic and Computer Design Fundamentals'' (3rd ed.), pp 453. Pearson Prentice Hall. .
Notes
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Binary arithmetic
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