Binary Numbers and Base Systems as Fast as Possible

Summary

The video explains how computers use binary (1s and 0s) through electricity to operate. It introduces the concept of positional notation in number systems, explaining how base 10 (decimal) works, then compares it to base 2 (binary). The video explores other numbering systems, like base 12 and base 36, and discusses how alphanumeric characters are used in systems like URL shorteners. It also touches on the historical preference for base 10 due to human anatomy, specifically our 10 fingers. Finally, the video promotes learning platforms like Lynda.com for further education.

Takeaways

• 🔌 Modern computers use binary, a system of 1s and 0s, to process information.
• 🔢 Our familiar decimal system, or base 10, uses ten symbols (0-9) and positional notation to represent numbers.
• 📚 Positional notation allows us to reuse the same digits in different positions to represent larger numbers, each position having a value ten times greater than the one to its right.
• 🛑 Binary, or base 2, operates on the same principles but uses only two symbols, with each new digit having a value twice as much as the one to its right.
• 💡 Binary counting is as simple as performing multiplication and addition, but it forms the basis for more complex computer operations.
• 🌐 There are many base systems beyond decimal and binary, such as base 8 or base 12, which can be more efficient for certain calculations.
• 🤔 The use of base 10 is likely due to humans having 10 fingers, a historical artifact rather than a practical choice.
• 🔤 When dealing with bases higher than 10, letters are used to represent numerals, leading to alphanumeric systems.
• 🔗 URL shorteners use a combination of numerals and letters to represent large numbers, allowing for the creation of short links from long URLs.
• 🎓 The video also promotes lynda.com as a valuable resource for learning new software and skills through structured, high-quality video tutorials.

Q & A

How do modern-day computers use electricity to function?

Modern-day computers use electricity by turning it on or off inside a microchip, represented by the binary symbols 1 and 0.

What is the significance of the binary system in computing?

The binary system is significant in computing because it provides a simple and efficient way to represent data using only two states, on and off, which correspond to the digits 1 and 0.

How does the decimal system (base 10) work?

The decimal system works by using 10 symbols (0-9) and a positional notation where each new digit to the left has a value ten times greater than the digit to its right.

Why do we use base 10 for our numerical system?

We use base 10 likely because humans have 10 fingers, which made counting and representing numbers in base 10 a natural choice.

What is positional notation and how does it apply to different base systems?

Positional notation is a method of representing numbers where each position has a value that is a multiple of the base. This principle applies to all base systems, whether it's base 10, binary, or any other base.

How is a binary number calculated?

A binary number is calculated by multiplying each digit by 2 raised to the power of its position, starting from 0 on the right, and then summing these values.

What are the advantages of using base systems other than base 10 for everyday math?

Base systems like base 8 and base 12 are advantageous for everyday math because they are more easily divisible than base 10, which can simplify calculations.

Why do we use letters to represent numerals in base systems with more than 10 digits?

Letters are used to represent numerals higher than 9 in base systems with more than 10 digits because there are not enough single symbols to represent all the values needed.

How do URL shorteners work?

URL shorteners work by representing a very large number using a combination of numerals and letters from the alphabet, allowing a long URL to be shortened into a more manageable form.

What is the maximum value that can be represented with 10 alphanumeric digits in a base 62 system?

With 10 alphanumeric digits in a base 62 system, the maximum value that can be represented is 14 million.

What is the connection between the concept of positional notation and the way URL shorteners encode large numbers?

The connection between positional notation and URL shorteners is that both use a base system to encode values, with URL shorteners using a base that includes letters to represent large numbers in a compact form.