#!/usr/bin/env python
# coding: utf-8

# **Note**: Click on "*Kernel*" > "*Restart Kernel and Clear All Outputs*" in [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) *before* reading this notebook to reset its output. If you cannot run this file on your machine, you may want to open it [in the cloud <img height="12" style="display: inline-block" src="../static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/main?urlpath=lab/tree/05_numbers/06_resources.ipynb).

# # Chapter 5: Numbers & Bits (Further Resources)

# ## Working with Bits

# The two videos below show how addition and multiplication works with numbers in their binary representations. Subtraction is a bit more involved as we need to understand how negative numbers are represented in binary with the concept of [Two's Complement <img height="12" style="display: inline-block" src="../static/link/to_wiki.png">](https://en.wikipedia.org/wiki/Two%27s_complement) first. A video on that is shown further below. Division in binary is actually also quite simple.

# In[1]:


from IPython.display import YouTubeVideo
YouTubeVideo("RgklPQ8rbkg", width="60%")


# In[2]:


YouTubeVideo("xHWKYFhhtJQ", width="60%")


# The video below explains the idea behind [Two's Complement <img height="12" style="display: inline-block" src="../static/link/to_wiki.png">](https://en.wikipedia.org/wiki/Two%27s_complement). This is how most modern programming languages implement negative integers. The video also shows how subtraction in binary works.

# In[3]:


YouTubeVideo("4qH4unVtJkE", width="60%")


# ## The Intuition behind Floating Point Numbers

# This video by the YouTube channel [Computerphile](https://www.youtube.com/channel/UC9-y-6csu5WGm29I7JiwpnA) explains floating point numbers in an intuitive way with some numeric examples.

# In[4]:


YouTubeVideo("PZRI1IfStY0", width="60%")


# ## An Introduction to Complex Numbers

# Below is a short introduction to [complex numbers <img height="12" style="display: inline-block" src="../static/link/to_wiki.png">](https://en.wikipedia.org/wiki/Complex_number) by [MIT](https://www.mit.edu) professor [Gilbert Strang <img height="12" style="display: inline-block" src="../static/link/to_wiki.png">](https://en.wikipedia.org/wiki/Gilbert_Strang) aimed at high school students.

# In[5]:


YouTubeVideo("Jkv-55ndVYY", width="60%")