Understanding offset-k method of representing negative integers
<p>I'm reading <a href="https://vineetgupta22.wordpress.com/tag/offset-binary-representation/" rel="nofollow noreferrer">this article</a> about offset-k method of representing negative integers. Can someone please explain the following passage using some examples:</p>
<blockquote>
<p>One logical way to represent signed integers is to have enough range
in binary numbers so that the zero can be offset to the middle of the
range of positive binary numbers. Then the magnitude of a negative
binary number can be simply subtracted from that zero point.</p>
</blockquote>
<p>I understand the mechanics, e.g. to represent number 4 in 11 bits, I'll do <code>4+1023=1027</code>, but can't understand the logic behind it and why it works.</p>