Editing Two's complement (section)

==Sign extension==
{{Main|Sign extension}}

{|class="wikitable floatright" style="margin-left: 1.5em;text-align:center"
|+ Sign-bit repetition in 7- and 8-bit integers using two's complement
|-
!Decimal
!7-bit notation
!8-bit notation
|-
|style="text-align:right"| −42 || 1010110 || 1101 0110
|-
|style="text-align:right"| 42 || 0101010 || 0010 1010
|}

When turning a two's-complement number with a certain number of bits into one with more bits (e.g., when copying from a one-byte variable to a two-byte variable), the most-significant bit must be repeated in all the extra bits. Some processors do this in a single instruction; on other processors, a conditional must be used followed by code to set the relevant bits or bytes.

Similarly, when a number is shifted to the right, the most-significant bit, which contains the sign information, must be maintained. However, when shifted to the left, a bit is shifted out. These rules preserve the common semantics that left shifts multiply the number by two and right shifts divide the number by two. However, if the most-significant bit changes from 0 to 1 (and vice versa), overflow is said to occur in the case that the value represents a signed integer.

Both shifting and doubling the precision are important for some multiplication algorithms. Note that unlike addition and subtraction, width extension and right shifting are done differently for signed and unsigned numbers.