Integers: Sign extension

We may need to change the number of bits used to represent a number.

For example, C has int, short int, and long int to represent integers.

The language doesn't specify the exact size of each form, but

sizeof (short int) <= sizeof (int) <= sizeof (long int)

How do we cast from one kind of int to a larger number of bits?

ints are represented in N-bit 2C

To convert a number from N bits to N + K bits in 2C notation,

copy (extend) the sign bit from bit N-1 to bit N + K -1

If the value is positive, all the higher-order bits will become 0;

if the value is negative, all the higher-order bits will become 1.

All of the other bits (location N-2, . . . , 0) remain unchanged.

Example:

3ten is 0011 in 4 bits

In 8 bits, it becomes 00000011 (the zero sign bit is extended to the left).

-3ten is 1101 in 4 bits

In 8 bits, it becomes 11111101 (the one sign bit is extended to the left).