16. Sign Extension

• Moving 2's complement integers between data types of different sizes is illegal without the sign extension operation.

• When necessary, you must sign-extend integer to convert signed value to a larger size.

• Sign-extending means copying the sign bit of the unextended value to all bits on the left side of the larger-size value.

• For example, 8-bit encoding of decimal number -56 can be sign-extended as follows:

                                 11001000 <- 8-bit value of -56
                        11111111 11001000 <- extended to 16-bit value
      11111111 11111111 11111111 11001000 <- extended 32-bit value
  

• The same way as leading zeroes do not affect values of a positive numbers, leading 1s do not affect values of a negative numbers.

• Sign-extend operation is often abbreviated SEXT.

• SEXT widens the data while maintaining its sign and value.

• Sign extending operation efficiently converts positive values as well, provided the sign bit is zero:

                                 01001000 <- 8-bit value of 72
                        00000000 01001000 <- extended to 16-bit value
      00000000 00000000 00000000 01001000 <- extended 32-bit value
  
  

• Note: it is programmer's responsibility to keep track of which values are signed or unsigned, and treat them accordingly.