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<p><a class="glightbox" href="../number_encoding.assets/1s_2s_complement.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Conversions between sign-magnitude, one's complement, and two's complement" class="animation-figure" src="../number_encoding.assets/1s_2s_complement.png" /></a></p>
<p align="center"> Figure 3-4 &nbsp; Conversions between sign-magnitude, one's complement, and two's complement </p>
<p>Although sign-magnitude is the most intuitive, it has limitations. For one, <strong>negative numbers in sign-magnitude cannot be directly used in calculations</strong>. For example, in sign-magnitude, calculating <span class="arithmatex">\(1 + (-2)\)</span> results in <span class="arithmatex">\(-3\)</span>, which is incorrect.</p>
<p>Although <u>sign-magnitude</u> is the most intuitive, it has limitations. For one, <strong>negative numbers in sign-magnitude cannot be directly used in calculations</strong>. For example, in sign-magnitude, calculating <span class="arithmatex">\(1 + (-2)\)</span> results in <span class="arithmatex">\(-3\)</span>, which is incorrect.</p>
<div class="arithmatex">\[
\begin{aligned}
&amp; 1 + (-2) \newline
@@ -3616,7 +3616,7 @@
&amp; \rightarrow -3
\end{aligned}
\]</div>
<p>To address this, computers introduced the <strong>one's complement</strong>. If we convert to one's complement and calculate <span class="arithmatex">\(1 + (-2)\)</span>, then convert the result back to sign-magnitude, we get the correct result of <span class="arithmatex">\(-1\)</span>.</p>
<p>To address this, computers introduced the <u>one's complement</u>. If we convert to one's complement and calculate <span class="arithmatex">\(1 + (-2)\)</span>, then convert the result back to sign-magnitude, we get the correct result of <span class="arithmatex">\(-1\)</span>.</p>
<div class="arithmatex">\[
\begin{aligned}
&amp; 1 + (-2) \newline
@@ -3634,7 +3634,7 @@
-0 &amp; \rightarrow 1000 \; 0000
\end{aligned}
\]</div>
<p>Like sign-magnitude, one's complement also suffers from the positive and negative zero ambiguity. Therefore, computers further introduced the <strong>two's complement</strong>. Let's observe the conversion process for negative zero in sign-magnitude, one's complement, and two's complement:</p>
<p>Like sign-magnitude, one's complement also suffers from the positive and negative zero ambiguity. Therefore, computers further introduced the <u>two's complement</u>. Let's observe the conversion process for negative zero in sign-magnitude, one's complement, and two's complement:</p>
<div class="arithmatex">\[
\begin{aligned}
-0 \rightarrow \; &amp; 1000 \; 0000 \; \text{(Sign-magnitude)} \newline
@@ -3919,7 +3919,7 @@ aria-label="Footer"
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