Beginner's Guide to Coding and Data

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Binary vs Decimal | Introducing positional numeral systems for programming beginners

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Exploring Positional Numeral Systems

Welcome, everyone! Today, we're diving into the fascinating world of positional numeral systems. While various bases exist, we'll focus mainly on decimal and binary.

  • Decimal: Base 10
  • Binary: Base 2

How Does It Work?

At its core, a positional numeral system allows us to represent numbers using digits and their positions. The position of each digit is crucial as it determines the value that each digit represents.

For example, in decimal, the position of each digit is based on powers of 10. In binary, the position of each digit is based on powers of 2.

Place Value
100 1
101 10
102 100
103 1000

The Importance of Bases

The concept of a base in a numeral system is key. It defines the number of symbols available for each digit and sets the place value of each digit. For example, in decimal, we have ten symbols (0-9), whereas in binary, we have just two (0 and 1).

Carrying Over

The process of carrying over values is integral to these systems. This mechanism enables us to create algorithms for mathematical operations like addition, subtraction, multiplication, and division.

Take decimal as an example: when we reach a sum of 10, we carry over to the next place value. This is similarly crucial in binary, where carry-over occurs more frequently.

Why It Matters

The carry-over feature is one significant reason why positional numeral systems are so broadly applicable today. These systems not only simplify arithmetic but also serve as the backbone for computing and numerous other fields.

Understanding positional numeral systems can offer insights into various disciplines, from math to computer science. In a future discussion, we'll explore numeral systems from base 2 to base 36 and discover some intriguing patterns.

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The carry over process is pretty huge. Humans figured that out and went with it. See how positional numeral systems work and why they are the primary way humans and machines represent numbers. The cool thing about the notebook is that we can change the number at the top or either one of the bases and the tables update in real-time. Give it a try here: https://beta.observablehq.com/@deeplizard/positional-numeral-systems Prerequisites videos: Numerical data explained - https://youtu.be/YDDqe60omL0 Numeral vs Number - https://youtu.be/RSdnNZBj8HQ πŸ•’πŸ¦Ž VIDEO SECTIONS πŸ¦ŽπŸ•’ 00:00 Welcome to DEEPLIZARD - Go to deeplizard.com for learning resources 00:30 Help deeplizard add video timestamps - See example in the description 05:45 Collective Intelligence and the DEEPLIZARD HIVEMIND πŸ’₯🦎 DEEPLIZARD COMMUNITY RESOURCES 🦎πŸ’₯ πŸ‘‹ Hey, we're Chris and Mandy, the creators of deeplizard! πŸ‘€ CHECK OUT OUR VLOG: πŸ”— https://youtube.com/deeplizardvlog πŸ’ͺ CHECK OUT OUR FITNESS CHANNEL: πŸ”— https://www.youtube.com/channel/UCdCxHNCexDrAx78VfAuyKiA 🧠 Use code DEEPLIZARD at checkout to receive 15% off your first Neurohacker order: πŸ”— https://neurohacker.com/shop?rfsn=6488344.d171c6 ❀️🦎 Special thanks to the following polymaths of the deeplizard hivemind: Mano Prime πŸ‘€ Follow deeplizard: Our vlog: https://youtube.com/deeplizardvlog Fitness: https://www.youtube.com/channel/UCdCxHNCexDrAx78VfAuyKiA Facebook: https://facebook.com/deeplizard Instagram: https://instagram.com/deeplizard Twitter: https://twitter.com/deeplizard Patreon: https://patreon.com/deeplizard YouTube: https://youtube.com/deeplizard πŸŽ“ Deep Learning with deeplizard: AI Art for Beginners - https://deeplizard.com/course/sdcpailzrd Deep Learning Dictionary - https://deeplizard.com/course/ddcpailzrd Deep Learning Fundamentals - https://deeplizard.com/course/dlcpailzrd Learn TensorFlow - https://deeplizard.com/course/tfcpailzrd Learn PyTorch - https://deeplizard.com/course/ptcpailzrd Natural Language Processing - https://deeplizard.com/course/txtcpailzrd Reinforcement Learning - https://deeplizard.com/course/rlcpailzrd Generative Adversarial Networks - https://deeplizard.com/course/gacpailzrd Stable Diffusion Masterclass - https://deeplizard.com/course/dicpailzrd πŸŽ“ Other Courses: DL Fundamentals Classic - https://deeplizard.com/learn/video/gZmobeGL0Yg Deep Learning Deployment - https://deeplizard.com/learn/video/SI1hVGvbbZ4 Data Science - https://deeplizard.com/learn/video/d11chG7Z-xk Trading - https://deeplizard.com/learn/video/ZpfCK_uHL9Y πŸ›’ Check out products deeplizard recommends on Amazon: πŸ”— https://amazon.com/shop/deeplizard πŸ“• Get a FREE 30-day Audible trial and 2 FREE audio books using deeplizard's link: πŸ”— https://amzn.to/2yoqWRn 🎡 deeplizard uses music by Kevin MacLeod πŸ”— https://youtube.com/channel/UCSZXFhRIx6b0dFX3xS8L1yQ ❀️ Please use the knowledge gained from deeplizard content for good, not evil.

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