What is sign extend?

Sign extend is a programming operation that involves extending the length of a binary number while preserving its sign. This operation is used when converting a binary number from a shorter length to a longer length, such as when a 16-bit number is converted to a 32-bit number.

During sign extend, the most significant bit (MSB) of the shorter binary number is examined. If the MSB is 1, the number is negative and its sign is preserved in the extended binary number by setting all the bits to the left of the original number's MSB to 1. If the MSB is 0, the number is positive and its sign is preserved by setting all the bits to the left of the original number's MSB to 0.

For example, if a 4-bit binary number 1101 is sign extended to 8 bits, the operation will result in the binary number 11111101, which represents the signed decimal number -3. This is because the MSB of the original 4-bit number is 1, indicating a negative value, and all the bits to the left of it are set to 1 to preserve the negative sign when extending the number to 8 bits.