Sign extension is the operation, in computer arithmetic, of increasing the number of bits of a binary number while preserving the number's sign (positive/negative). This is done by appending digits to the most significant side of the number, following a procedure dependent on the particular signed number representation used. A computer is a machine capable of processing data according to a program — a list of instructions. ... Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though professional mathematicians often treat arithmetic as a synonym for number theory. ... This article is about the unit of information. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... A negative number is a number that is less than zero, such as −3. ... The binary representation of decimal 149, with the MSB highlighted. ... Comparison of Integer Representations in 4-bit In mathematics, negative numbers in any base are represented in the usual way, by prefixing them with a − sign. ...

For example, if six bits are used to represent the number +10 (binary: 001010) and the sign extend operation increases the word length to 16 bits, then the new representation is simply 0000 0000 0000 1010 (assuming the left side is the most significant bit). Thus, the fact that the original value was positive is still maintained. If ten bits are used to represent the value -15 using two's complement (11 1111 0001), and again sign extend to 16 is used, the new representation would be 1111 1111 1111 0001. Thus, by padding the left side with ones, the negativeness of the original number is maintained. In computing, word is a term for the natural unit of data used by a particular computer design. ... Twos complement is the most popular method of signifying negative integers in computer science. ...

In the x86 instruction set used by the main microprocessors of all common PCs, sign extension is done by the instructions cbw, cwd, cwde, and cdq ("convert byte to word", "c. word to doubleword", "c. w. to extended dw.", and "c. dw. 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). // Introduction The x86 instruction set has undergone numerous changes over time. ... Microprocessors, including an Intel 80486DX2 and an Intel 80386 A microprocessor (sometimes abbreviated µP) is a digital electronic component with miniaturized transistors on a single semiconductor integrated circuit (IC). ... One of the first PCs from IBM - the IBM PC model 5150. ...

References

• Mano, Morris M.; Kime, Charles R. (2004). Logic and Computer Design Fundamentals (3rd ed.), pp 453. Pearson Prentice Hall. ISBN 0-13-140539-X.