Sign Extension
Sign extension is the process of extending the sign bit of a signed binary number to fill additional bits when converting from one size to another. It is commonly used when converting a signed integer from a smaller size to a larger size.

Converting a Signed Integer
When converting a signed integer from one size to another, it is important to preserve the sign of the original number. Sign extension ensures that the sign bit is correctly propagated to the additional bits, maintaining the original value of the number.

Process of Sign Extension
The sign extension process depends on the original size of the signed integer and the desired size after conversion. Here is a step-by-step explanation of the sign extension process:

1. Determine the original size of the signed integer, which is usually represented in bits.
2. Determine the desired size after conversion, which is also represented in bits.
3. Check the sign bit of the original number. If it is 0, the number is positive. If it is 1, the number is negative.
4. If the original size is smaller than the desired size, sign extension is required.
5. To extend the sign bit, copy it to all the additional bits.
6. If the number is positive (sign bit is 0), copy 0 to all the additional bits.
7. If the number is negative (sign bit is 1), copy 1 to all the additional bits.
8. Repeat the process until the desired size is reached.

Example
Let's consider an example to understand the sign extension process. Suppose we have a signed 8-bit integer with the value -5 (-00000101 in binary) and we want to convert it to a signed 16-bit integer.

1. The original size is 8 bits and the desired size is 16 bits.
2. The sign bit of the original number is 1, indicating a negative value.
3. To extend the sign bit, we copy 1 to all the additional 8 bits.
4. The resulting signed 16-bit integer is -5 (-0000000000000101 in binary).

This sign extension ensures that the negative value is preserved during the conversion process and the resulting number is correctly represented in the larger size.

In conclusion, sign extension is the step involved in converting a signed integer from one size to another. It ensures that the sign bit is correctly propagated to the additional bits, preserving the original value of the number.