Weird Number in Two's Complement

The binary number 100..000₂ is called a weird number because after inverting and adding 1 (taking the two's complement) it does not change.

100..000  inverting
011..111
+ 1
------------
100..000

This number (100..00₂ = -2^N-1) is the most negative of two's complement numbers. And it has no positive counterpart.

Harris D. M., Harris S. L. - Digital Design and Computer Architecture, 2nd Edition - 2012
1.4.6 Signed Binary Numbers - 15 page

Resources

• Three Ideas of Signed Binary Numbers
• Crash Due to Overflow
• Twos Complement Overflow
• Range Number Systems
• Sign Extension