Sign extension of binary vector

• Signed numbers are converted to a larger data type using this method
• Add copies of the most significant bit (MSB) to the representation

Example

char x = -56; // 0xC8 -> 0b11001000
 
short y = (short) x; // 0xFFC8 -> 0b1111111111001000

Visual representation

• The following figure shows an example of sign extending from $w=3$ to $w=4$. ($w$ → word size). Notice that the combined weights of the upper two bits ($w=4$) is $-8+4=-4$, which matches the weight of the sign bit for $w=3$.

Sources

• Computer Systems - A Programmer’s Perspective

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