de-soot · de-soot · Dec 9, 2025 · Dec 8, 2025
diff --git a/Gemfile.lock b/Gemfile.lock
@@ -1,7 +1,7 @@
 GEM
   remote: https://rubygems.org/
   specs:
-    activesupport (8.1.0)
+    activesupport (8.1.1)
       base64
       bigdecimal
       concurrent-ruby (~> 1.0, >= 1.3.1)
@@ -14,8 +14,8 @@ GEM
       securerandom (>= 0.3)
       tzinfo (~> 2.0, >= 2.0.5)
       uri (>= 0.13.1)
-    addressable (2.8.7)
-      public_suffix (>= 2.0.2, < 7.0)
+    addressable (2.8.8)
+      public_suffix (>= 2.0.2, < 8.0)
     base64 (0.3.0)
     bigdecimal (3.3.1)
     coffee-script (2.4.1)
@@ -25,26 +25,27 @@ GEM
     colorator (1.1.0)
     commonmarker (0.23.12)
     concurrent-ruby (1.3.5)
-    connection_pool (2.5.4)
+    connection_pool (3.0.2)
     csv (3.3.5)
-    dnsruby (1.73.0)
+    dnsruby (1.73.1)
       base64 (>= 0.2)
       logger (~> 1.6)
       simpleidn (~> 0.2.1)
     drb (2.2.3)
     em-websocket (0.5.3)
       eventmachine (>= 0.12.9)
       http_parser.rb (~> 0)
-    ethon (0.17.0)
+    ethon (0.18.0)
       ffi (>= 1.15.0)
+      logger
     eventmachine (1.2.7)
     execjs (2.10.0)
     faraday (2.14.0)
       faraday-net_http (>= 2.0, < 3.5)
       json
       logger
-    faraday-net_http (3.4.1)
-      net-http (>= 0.5.0)
+    faraday-net_http (3.4.2)
+      net-http (~> 0.5)
     ffi (1.17.2-x64-mingw-ucrt)
     ffi (1.17.2-x86_64-linux-gnu)
     forwardable-extended (2.6.0)
@@ -217,7 +218,7 @@ GEM
       gemoji (>= 3, < 5)
       html-pipeline (~> 2.2)
       jekyll (>= 3.0, < 5.0)
-    json (2.15.1)
+    json (2.17.1)
     kramdown (2.4.0)
       rexml
     kramdown-parser-gfm (1.1.0)
@@ -232,9 +233,9 @@ GEM
       jekyll (>= 3.5, < 5.0)
       jekyll-feed (~> 0.9)
       jekyll-seo-tag (~> 2.1)
-    minitest (5.26.0)
-    net-http (0.6.0)
-      uri
+    minitest (5.26.2)
+    net-http (0.8.0)
+      uri (>= 0.11.1)
     nokogiri (1.18.10-x64-mingw-ucrt)
       racc (~> 1.4)
     nokogiri (1.18.10-x86_64-linux-gnu)
@@ -258,7 +259,7 @@ GEM
     sass-listen (4.0.0)
       rb-fsevent (~> 0.9, >= 0.9.4)
       rb-inotify (~> 0.9, >= 0.9.7)
-    sawyer (0.9.2)
+    sawyer (0.9.3)
       addressable (>= 2.3.5)
       faraday (>= 0.17.3, < 3)
     securerandom (0.4.1)
@@ -269,12 +270,9 @@ GEM
       ethon (>= 0.9.0)
     tzinfo (2.0.6)
       concurrent-ruby (~> 1.0)
-    tzinfo-data (1.2025.2)
-      tzinfo (>= 1.0.0)
     unicode-display_width (1.8.0)
-    uri (1.0.4)
-    wdm (0.1.1)
-    webrick (1.9.1)
+    uri (1.1.1)
+    webrick (1.9.2)
 
 PLATFORMS
   x64-mingw-ucrt

diff --git a/README.md b/README.md
@@ -10,24 +10,23 @@ Click [here](https://de-soot.github.io)
 
 ### Run Locally
 
-1) [Clone](https://docs.github.com/en/get-started/getting-started-with-git/about-remote-repositories) this github repository onto your computer by simply downloading the source code from this Github repository, or by using [`git`](https://git-scm.com):
+1. [Clone](https://docs.github.com/en/get-started/getting-started-with-git/about-remote-repositories) this github repository onto your computer by simply downloading the source code from this Github repository, or by using [`git`](https://git-scm.com):
 ```sh
 git clone https://github.com/de-soot/de-soot.github.io
 ```
-2) Follow [this guide](https://jekyllrb.com/docs/installation) to install the prerequisites for Jekyll for your system if you have not already done so.
-3) Once all requirements are installed, run the following command below in a command line terminal:
+2. Follow [this guide](https://jekyllrb.com/docs/installation) to install the prerequisites for Jekyll for your system if you have not already done so.
+3. Once all requirements are installed, run the following command below in a command line terminal:
 ```sh
 gem install jekyll bundler
 ```
-4) Now that everything's installed and good to go, navigate the terminal to the directory where the you downloaded the copy of the Github repository, like so:
+4. Now that everything's installed, navigate the terminal to the directory of the copy of the Github repository:
 ```sh
 cd [Path of source code folder]
 ```
-5) Enter this command:
+5. Enter this command to preview the site:
 ```sh
 bundle exec jekyll serve
 ```
-6) Navigate to http://localhost:4000 in a browser.
-7) Profit!
-
-Refer to the [official Jekyll documentation](https://jekyllrb.com/docs) for more information regarding installing and running Jekyll.
+6. Navigate to http://localhost:4000 in a browser.
+7. Add your own Markdown posts inside `_posts`.
+8. Profit!
diff --git a/_config.yml b/_config.yml
@@ -19,8 +19,8 @@
 # in the templates via {{ site.myvariable }}.
 
 title: de_soot
-github_username:  de-soot
-description: Hosted on Github Pages
+github_username: de-soot
+description: Technical blog
 baseurl: "" # the subpath of your site, e.g. /blog
 url: "https://de-soot.github.io" # the base hostname & protocol for your site, e.g. http://example.com
 domain: de-soot.github.io

diff --git a/_posts/2025-02-20-groff-apa.md b/_posts/2025-02-20-groff-apa.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: Guide to APA with groff ms and refer
-date: 2025-02-07
+date: 2025-02-20
 categories: groff, ms, refer, macro, tmac, APA, style guide, pdf
 permalink: /groff-apa
 ---

diff --git a/_posts/2025-12-08-2s-complement.md b/_posts/2025-12-08-2s-complement.md
@@ -0,0 +1,38 @@
+---
+layout: post
+title: 2's Complement Derivation
+date: 2025-12-08
+categories: cs, binary, bits, negative numbers, derivation, proof, math, 2's complement
+permalink: /2s-complement
+---
+
+If you have ever taken CS in high school or college, you have probably been taught about how to represent negative numbers in binary using 2's complement.
+
+But teachers generally just tell you to "flip the bits and add one" without really explaining why it works---similar to how high school teachers treat math formulas.
+
+I have never liked memorising without understanding when it comes to learning, so I came up with an intuitive derivation and wrote this blog post to share it in hopes that somebody may find it useful.
+
+## How Does 2's Complement Work?
+
+Say there is a number `x` represented by `n` binary digits (bits).
+Since each bit can be `0` or `1`, there are 2^n possible combinations for the string of bits that represent values ranging from zero to 2^n - 1, and thus `x` is always less than 2^n.
+
+If we flip all the bits of `x` using the bitwise NOT operator (`~`), we get a new number with `1` bits where there were `0`'s in `x` and `0` bits where there were `1`'s in `x`.
+We will call this new number `~x`, where `x + ~x = 2^n - 1`, since 2^n - 1 has all `n` number of bits set to `1`.
+
+Rearranging the above equation for `x`, we get `x = (2^n - 1) - ~x`.
+It is then easy to find that `-x = -(2^n - 1 - ~x) = -2^n + 1 + ~x`.
+Now see the picture of where "flip the bits and add one" comes from.
+
+But we cannot just flip bits and add 1 to get `-x` with ordinary bits, that would just be `~x + 1`.
+We are still missing the `-2^n` in the equation, but how would we get that?
+
+Currently, since the value of the most significant bit is `2^(n-1)`, if we add another bit from the left, its place value would be `2^(n-1) * 2 = 2^n`.
+Now all we have to do is define the value of that new bit to be negative to get `-2^n`.
+When we flip the bits of `x`, this new bit we added will also get flipped along with it.
+
+## Conclusion
+
+Putting all the pieces together, we get that for a number `x` represented by `n` bits (with an extra bit having a place value of `-2^n`) where `x = (2^n - 1) - ~x`, you would need to flip its bits and add one to get `-2^n + ~x + 1 = -x`.
+
+Hopefully after reading this, you will have gained a better understanding of using 2's complement for converting binary numbers to negative.
diff --git a/_site/404.html b/_site/404.html
@@ -3,20 +3,20 @@
   <meta charset="utf-8">
   <meta http-equiv="X-UA-Compatible" content="IE=edge">
   <meta name="viewport" content="width=device-width, initial-scale=1"><!-- Begin Jekyll SEO tag v2.8.0 -->
-<title>de_soot | Hosted on Github Pages</title>
+<title>de_soot | Technical blog</title>
 <meta name="generator" content="Jekyll v3.10.0" />
 <meta property="og:title" content="de_soot" />
 <meta property="og:locale" content="en_US" />
-<meta name="description" content="Hosted on Github Pages" />
-<meta property="og:description" content="Hosted on Github Pages" />
+<meta name="description" content="Technical blog" />
+<meta property="og:description" content="Technical blog" />
 <link rel="canonical" href="http://localhost:4000/404.html" />
 <meta property="og:url" content="http://localhost:4000/404.html" />
 <meta property="og:site_name" content="de_soot" />
 <meta property="og:type" content="website" />
 <meta name="twitter:card" content="summary" />
 <meta property="twitter:title" content="de_soot" />
 <script type="application/ld+json">
-{"@context":"https://schema.org","@type":"WebPage","description":"Hosted on Github Pages","headline":"de_soot","url":"http://localhost:4000/404.html"}</script>
+{"@context":"https://schema.org","@type":"WebPage","description":"Technical blog","headline":"de_soot","url":"http://localhost:4000/404.html"}</script>
 <!-- End Jekyll SEO tag -->
 <link rel="stylesheet" href="/assets/main.css"><link type="application/atom+xml" rel="alternate" href="http://localhost:4000/feed.xml" title="de_soot" /></head>
 <body><header class="site-header" role="banner">
@@ -75,7 +75,7 @@ <h2 class="footer-heading">de_soot</h2>
 </div>
 
       <div class="footer-col footer-col-3">
-        <p>Hosted on Github Pages</p>
+        <p>Technical blog</p>
       </div>
     </div>
 

diff --git a/_site/README.md b/_site/README.md
@@ -1,6 +1,6 @@
 # de-soot.github.io
 
-A place on the Internet where I write about stuff.
+Personal website where I write technical blog posts.
 
 ## Usage
 
@@ -10,24 +10,23 @@ Click [here](https://de-soot.github.io)
 
 ### Run Locally
 
-1) [Clone](https://docs.github.com/en/get-started/getting-started-with-git/about-remote-repositories) this github repository onto your computer by simply downloading the source code from this Github repository, or by using [`git`](https://git-scm.com):
+1. [Clone](https://docs.github.com/en/get-started/getting-started-with-git/about-remote-repositories) this github repository onto your computer by simply downloading the source code from this Github repository, or by using [`git`](https://git-scm.com):
 ```sh
 git clone https://github.com/de-soot/de-soot.github.io
 ```
-2) Follow [this guide](https://jekyllrb.com/docs/installation) to install the prerequisites for Jekyll for your system if you have not already done so.
-3) Once all requirements are installed, run the following command below in a command line terminal:
+2. Follow [this guide](https://jekyllrb.com/docs/installation) to install the prerequisites for Jekyll for your system if you have not already done so.
+3. Once all requirements are installed, run the following command below in a command line terminal:
 ```sh
 gem install jekyll bundler
 ```
-4) Now that everything's installed and good to go, navigate the terminal to the directory where the you downloaded the copy of the Github repository, like so:
+4. Now that everything's installed, navigate the terminal to the directory of the copy of the Github repository:
 ```sh
-cd "{Path of source code folder}"
+cd [Path of source code folder]
 ```
-5) Enter this command:
+5. Enter this command to preview the site:
 ```sh
 bundle exec jekyll serve
 ```
-6) Navigate to http://localhost:4000 in a browser.
-7) Profit!
-
-Refer to the [official Jekyll documentation](https://jekyllrb.com/docs) for more information regarding installing and running Jekyll.
+6. Navigate to http://localhost:4000 in a browser.
+7. Add your own Markdown posts inside `_posts`.
+8. Profit!
diff --git a/_site/about.html b/_site/about.html
@@ -7,16 +7,16 @@
 <meta name="generator" content="Jekyll v3.10.0" />
 <meta property="og:title" content="About" />
 <meta property="og:locale" content="en_US" />
-<meta name="description" content="Hosted on Github Pages" />
-<meta property="og:description" content="Hosted on Github Pages" />
+<meta name="description" content="Technical blog" />
+<meta property="og:description" content="Technical blog" />
 <link rel="canonical" href="http://localhost:4000/about" />
 <meta property="og:url" content="http://localhost:4000/about" />
 <meta property="og:site_name" content="de_soot" />
 <meta property="og:type" content="website" />
 <meta name="twitter:card" content="summary" />
 <meta property="twitter:title" content="About" />
 <script type="application/ld+json">
-{"@context":"https://schema.org","@type":"WebPage","description":"Hosted on Github Pages","headline":"About","url":"http://localhost:4000/about"}</script>
+{"@context":"https://schema.org","@type":"WebPage","description":"Technical blog","headline":"About","url":"http://localhost:4000/about"}</script>
 <!-- End Jekyll SEO tag -->
 <link rel="stylesheet" href="/assets/main.css"><link type="application/atom+xml" rel="alternate" href="http://localhost:4000/feed.xml" title="de_soot" /></head>
 <body><header class="site-header" role="banner">
@@ -70,7 +70,7 @@ <h2 class="footer-heading">de_soot</h2>
 </div>
 
       <div class="footer-col footer-col-3">
-        <p>Hosted on Github Pages</p>
+        <p>Technical blog</p>
       </div>
     </div>
 

diff --git a/_site/dark-mode.html b/_site/dark-mode.html
@@ -192,7 +192,7 @@ <h2 class="footer-heading">de_soot</h2>
 </div>
 
       <div class="footer-col footer-col-3">
-        <p>Hosted on Github Pages</p>
+        <p>Technical blog</p>
       </div>
     </div>
 

diff --git a/_site/feed.xml b/_site/feed.xml
@@ -1,4 +1,33 @@
-<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" ><generator uri="https://jekyllrb.com/" version="3.10.0">Jekyll</generator><link href="http://localhost:4000/feed.xml" rel="self" type="application/atom+xml" /><link href="http://localhost:4000/" rel="alternate" type="text/html" /><updated>2025-12-04T17:22:50+08:00</updated><id>http://localhost:4000/feed.xml</id><title type="html">de_soot</title><subtitle>Hosted on Github Pages</subtitle><entry><title type="html">Guide to APA with groff ms and refer</title><link href="http://localhost:4000/groff-apa" rel="alternate" type="text/html" title="Guide to APA with groff ms and refer" /><published>2025-02-07T00:00:00+08:00</published><updated>2025-02-07T00:00:00+08:00</updated><id>http://localhost:4000/groff-apa</id><content type="html" xml:base="http://localhost:4000/groff-apa"><![CDATA[<p>This guide explains why and how I used groff with the ms and refer macros to write my college essay in Neovim.</p>
+<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" ><generator uri="https://jekyllrb.com/" version="3.10.0">Jekyll</generator><link href="http://localhost:4000/feed.xml" rel="self" type="application/atom+xml" /><link href="http://localhost:4000/" rel="alternate" type="text/html" /><updated>2025-12-08T21:47:51+08:00</updated><id>http://localhost:4000/feed.xml</id><title type="html">de_soot</title><subtitle>Technical blog</subtitle><entry><title type="html">2’s Complement Derivation</title><link href="http://localhost:4000/2s-complement" rel="alternate" type="text/html" title="2’s Complement Derivation" /><published>2025-12-08T00:00:00+08:00</published><updated>2025-12-08T00:00:00+08:00</updated><id>http://localhost:4000/2s-complement</id><content type="html" xml:base="http://localhost:4000/2s-complement"><![CDATA[<p>If you have ever taken CS in high school or college, you have probably been taught about how to represent negative numbers in binary using 2’s complement.</p>
+
+<p>But teachers generally just tell you to “flip the bits and add one” without really explaining why it works—similar to how high school teachers treat math formulas.</p>
+
+<p>I have never liked memorising without understanding when it comes to learning, so I came up with an intuitive derivation and wrote this blog post to share it in hopes that somebody may find it useful.</p>
+
+<h2 id="how-does-2s-complement-work">How Does 2’s Complement Work?</h2>
+
+<p>Say there is a number <code class="language-plaintext highlighter-rouge">x</code> represented by <code class="language-plaintext highlighter-rouge">n</code> binary digits (bits).
+Since each bit can be <code class="language-plaintext highlighter-rouge">0</code> or <code class="language-plaintext highlighter-rouge">1</code>, there are 2^n possible combinations for the string of bits that represent values ranging from zero to 2^n - 1, and thus <code class="language-plaintext highlighter-rouge">x</code> is always less than 2^n.</p>
+
+<p>If we flip all the bits of <code class="language-plaintext highlighter-rouge">x</code> using the bitwise NOT operator (<code class="language-plaintext highlighter-rouge">~</code>), we get a new number with <code class="language-plaintext highlighter-rouge">1</code> bits where there were <code class="language-plaintext highlighter-rouge">0</code>’s in <code class="language-plaintext highlighter-rouge">x</code> and <code class="language-plaintext highlighter-rouge">0</code> bits where there were <code class="language-plaintext highlighter-rouge">1</code>’s in <code class="language-plaintext highlighter-rouge">x</code>.
+We will call this new number <code class="language-plaintext highlighter-rouge">~x</code>, where <code class="language-plaintext highlighter-rouge">x + ~x = 2^n - 1</code>, since 2^n - 1 has all <code class="language-plaintext highlighter-rouge">n</code> number of bits set to <code class="language-plaintext highlighter-rouge">1</code>.</p>
+
+<p>Rearranging the above equation for <code class="language-plaintext highlighter-rouge">x</code>, we get <code class="language-plaintext highlighter-rouge">x = (2^n - 1) - ~x</code>.
+It is then easy to find that <code class="language-plaintext highlighter-rouge">-x = -(2^n - 1 - ~x) = -2^n + 1 + ~x</code>.
+Now see the picture of where “flip the bits and add one” comes from.</p>
+
+<p>But we cannot just flip bits and add 1 to get <code class="language-plaintext highlighter-rouge">-x</code> with ordinary bits, that would just be <code class="language-plaintext highlighter-rouge">~x + 1</code>.
+We are still missing the <code class="language-plaintext highlighter-rouge">-2^n</code> in the equation, but how would we get that?</p>
+
+<p>Currently, since the value of the most significant bit is <code class="language-plaintext highlighter-rouge">2^(n-1)</code>, if we add another bit from the left, its place value would be <code class="language-plaintext highlighter-rouge">2^(n-1) * 2 = 2^n</code>.
+Now all we have to do is define the value of that new bit to be negative to get <code class="language-plaintext highlighter-rouge">-2^n</code>.
+When we flip the bits of <code class="language-plaintext highlighter-rouge">x</code>, this new bit we added will also get flipped along with it.</p>
+
+<h2 id="conclusion">Conclusion</h2>
+
+<p>Putting all the pieces together, we get that for a number <code class="language-plaintext highlighter-rouge">x</code> represented by <code class="language-plaintext highlighter-rouge">n</code> bits (with an extra bit having a place value of <code class="language-plaintext highlighter-rouge">-2^n</code>) where <code class="language-plaintext highlighter-rouge">x = (2^n - 1) - ~x</code>, you would need to flip its bits and add one to get <code class="language-plaintext highlighter-rouge">-2^n + ~x + 1 = -x</code>.</p>
+
+<p>Hopefully after reading this, you will have gained a better understanding of using 2’s complement for converting binary numbers to negative.</p>]]></content><author><name></name></author><category term="cs," /><category term="binary," /><category term="bits," /><category term="negative" /><category term="numbers," /><category term="derivation," /><category term="proof," /><category term="math," /><category term="2&apos;s" /><category term="complement" /><summary type="html"><![CDATA[If you have ever taken CS in high school or college, you have probably been taught about how to represent negative numbers in binary using 2’s complement.]]></summary></entry><entry><title type="html">Guide to APA with groff ms and refer</title><link href="http://localhost:4000/groff-apa" rel="alternate" type="text/html" title="Guide to APA with groff ms and refer" /><published>2025-02-20T00:00:00+08:00</published><updated>2025-02-20T00:00:00+08:00</updated><id>http://localhost:4000/groff-apa</id><content type="html" xml:base="http://localhost:4000/groff-apa"><![CDATA[<p>This guide explains why and how I used groff with the ms and refer macros to write my college essay in Neovim.</p>
 
 <h1 id="table-of-contents-">Table of Contents <a name="tableofcontents"></a></h1>
-Original file line number
+Diff line change
@@ Expand Up / @@ -192,7 +192,7 @@ <h2 class="footer-heading">de_soot</h2> @@
     </div>
           <div class="footer-col footer-col-3">
-            <p>Hosted on Github Pages</p>
+            <p>Technical blog</p>
           </div>
         </div>
@@ Expand Down @@