Binary Numbers and Base Systems as Fast as Possible
Summary
TLDRThe 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.
Outlines
🔢 Understanding Binary and Base 10 Systems
This paragraph introduces the concept of how modern computers use electricity, which is represented as binary (1 and 0) inside a microchip. The author explains how binary works by comparing it to our familiar base 10 system. They describe positional notation in the base 10 system, where each new digit represents a value 10 times greater than the previous one. This logic applies to binary as well, where the two symbols (0 and 1) follow the same principle. The paragraph concludes by explaining how binary calculations work through multiplication and addition of the digit positions.
✍️ A Brief History of Number Systems and Alphanumerics
The second part delves into the history and reasoning behind the use of the base 10 system, which likely originated from humans having 10 fingers. While other systems like base 8 or base 12 are more efficient for division, base 10 became the standard. The author briefly touches on the superiority of the metric system before transitioning into how higher base systems, such as base 12 and beyond, utilize letters to represent numerals greater than 9. They explain that alphanumeric systems are used for large numbers, like in URL shorteners, allowing for an immense range of possible values with fewer characters.
Mindmap
Keywords
💡Binary
💡Decimal
💡Positional Notation
💡Bits and Bytes
💡Boolean Logic
💡ASCII
💡Base Systems
💡Alphanumeric
💡URL Shorteners
💡Metric System
Highlights
Modern-day computers use binary, represented by 1s and 0s, to process information.
Decimal system uses 10 symbols, while binary uses only two.
Positional notation is a system where each digit's value is ten times greater than the digit to its right.
Binary counting involves simple multiplication and addition.
The complexity of computing increases with concepts like bits, bytes, boolean logic, and ASCII.
Other base systems like base 2, 3, 4, and 5 operate on the same principles as the decimal system.
Base 10 is used likely because humans have 10 fingers.
Base 8 and base 12 are more divisible and could be superior for everyday math.
Switching from base 10 would be as difficult as changing the imperial system to metric.
Base 12 and higher systems use letters to represent numerals higher than 9, forming alphanumeric characters.
URL shorteners use a combination of numerals and letters to represent large numbers.
Base 36 can represent numbers up to 14 million with only four digits.
With 10 digits, base 62 can represent up to 839 quadrillion possible values.
Lynda.com is recommended for learning new software and skills with high-quality video tutorials.
Lynda.com offers a wide variety of subjects and software tutorials.
Access to Lynda.com starts at $25 a month, with a free 7-day trial available.
Transcripts
modern-day computers use electricity to
work and inside of a microchip
electricity is turned either on or off
which is represented by the symbols 1
and 0. this is called binary you've
probably heard of binary already and
that that's how computers work but do
you know how binary works well you're
about to find out but first we need to
understand exactly how our numerical
base system known as decimal or base 10
works the way it does so there are 10
count em 10 symbols that we use for all
of our numbers starting from 0 we can
count all the way up to 9 before we run
out of symbols to use now we could just
keep adding symbols at this point but
that would get out of hand very quickly
i mean can you imagine having to
memorize a specific symbol for every
single number that's ridiculous and
that's why we reuse the same symbols
over and over again in a very clever
system called positional notation so in
the base 10 system as soon as we get to
10 or an exponent of 10 we need to add
another digit to the left of our current
digit because there are 10 symbols each
new digit has to have a value 10 times
greater than the digit to its right so
that's using 10 symbols but what if you
had only two symbols to work with well
then everything that i said still
applies with just two symbols each new
digit needs to have a value two times
greater than the digit to its right
so a sequence like this would equal 1
times 128 plus 1 times 16 plus 1 times 8
plus 1 times 2 plus 1 which is
155
and that's how you count in binary it's
actually really simple it's just
multiplication and addition now it gets
a lot more complicated from here with
bits and bytes and boolean logic and
ascii and the list just goes on and on
so let's return to base systems there
are a lot of ways to write numbers other
than decimal and binary you've got base
two base three base four base five i
could go on they all work with the same
principles of positional notation so you
might be wondering with all these
numbering systems to choose from why do
we use base 10 that's a good question
this goes all the way back to roman
numerals and egyptian hieroglyphs it's
likely that we use base 10 simply
because we have
10 fingers also known as digits other
base systems like base 8 and base 12 are
actually superior for simple everyday
math since 8 and 12 are much more easily
divisible than 10 but it's definitely
too late to change our minds about using
base 10 we'll probably be stuck with it
forever switching away from it now would
be even harder than trying to convince
america to drop the imperial system and
finally switch to metric you know like
the rest of the civilized world like
yeah the metric system is superior but
who's going to tell america what to do
now if you're going to be using base 12
or any other base system with more than
10 digits it's standard to use letters
to represent numerals higher than 9. so
10 is a 11 is b 12 is c and so on this
is called alphanumeric you know those
url shorteners that you see on twitter
and elsewhere have you ever wondered how
they work all those jumbled characters
really just represent a very large
number by using numerals and every
letter of the alphabet you can get all
the way up to base 36 using lowercase
and uppercase letters gives you base 62
and with that you can get all the way up
to 14 million with only four digits with
just 10 digits you can get up to
839 quadrillion possible values that's a
lot of shortened urls so you just
learned about positional notation binary
numbers numeral based systems
alphanumeric characters and url
shorteners i hope you enjoyed it and if
you're in the mood for more learning
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