CCNA - Converting Between Binary and Decimal Numbering Systems
Summary
TLDRThis video explains the process of converting numbers between the decimal (base 10) and binary (base 2) systems. It begins by discussing place values in the decimal system, where numbers are based on powers of ten, and then compares it to the binary system, which only uses two digits (0 and 1). The video walks through examples of converting decimal numbers like 168 to binary and vice versa, including how to interpret binary numbers in IP addresses. The focus is on understanding place values and simplifying the conversion process for easy comprehension.
Takeaways
- 🔢 The video explains binary to decimal conversion, starting with a review of positional notation or place values.
- 💡 In the decimal system (base 10), each digit represents powers of 10, such as the ones, tens, hundreds, and thousands places.
- ✏️ The number 2168 can be broken down into place values: 2 in the thousands place, 1 in the hundreds place, 6 in the tens place, and 8 in the ones place.
- 🔍 The decimal system uses ten numerals (0-9) in each place value, making it a base-10 system.
- ⚙️ Binary is a base-2 system with only two numerals: 0 and 1. Each place value represents powers of 2.
- 📊 The place values in binary correspond to powers of 2, such as 2^0 = 1, 2^1 = 2, 2^2 = 4, up to 2^7 = 128 for an 8-bit byte.
- 💻 To convert decimal to binary, find the place values where 1 is needed. For example, 168 in binary is 10101000.
- 🔄 The process for converting binary to decimal involves adding up the place values for the positions where a 1 appears. For example, binary 01101101 equals decimal 109.
- 🌐 The video demonstrates how to convert a binary IP address to decimal. Each octet is calculated separately, such as 11000000 for 192.
- 📊 In the example, the binary IP address 11000000.10101000.00000001.01100101 converts to the decimal IP address 192.168.1.101.
Q & A
What is the significance of place values in the decimal number system?
-In the decimal system, place values determine the value of a digit based on its position. Each place represents powers of ten, such as ones, tens, hundreds, and thousands.
How are the powers of ten related to the place values in the decimal system?
-In the decimal system, each place value is a power of ten. For example, the ones place is 10^0, the tens place is 10^1, the hundreds place is 10^2, and so on.
What does the number 2168 represent in terms of its place values?
-The number 2168 represents 2 in the thousands place (2000), 1 in the hundreds place (100), 6 in the tens place (60), and 8 in the ones place (8). Added together, this equals 2168.
How is binary different from the decimal system?
-Binary is a base-2 system that uses only two digits, 0 and 1, whereas the decimal system is base-10 and uses digits from 0 to 9. Each place value in binary represents a power of 2.
What are the place values in the binary system?
-In binary, the place values are based on powers of 2, such as 2^0 (1), 2^1 (2), 2^2 (4), 2^3 (8), 2^4 (16), 2^5 (32), 2^6 (64), and 2^7 (128).
How do you convert the decimal number 168 into binary?
-To convert 168 to binary, you identify which powers of 2 sum to 168. This gives 128 (2^7), 32 (2^5), and 8 (2^3), so 168 in binary is 10101000.
What is the process of converting a binary number to decimal?
-To convert binary to decimal, multiply each binary digit by its corresponding power of 2 and sum the values. For example, the binary number 01101101 converts to decimal as 109.
How would you convert the binary number 01101101 to decimal?
-The binary number 01101101 equals 64 + 32 + 8 + 4 + 1, which totals 109 in decimal.
What is an IP address, and how is it represented in binary?
-An IP address is a 32-bit number divided into four 8-bit segments, or octets. Each octet can be represented in binary, and then converted to decimal for easier reading.
How do you convert a binary IP address to its decimal form?
-To convert a binary IP address to decimal, convert each 8-bit binary octet individually to its decimal equivalent, and then combine the four decimal numbers. For example, the binary IP 11000000.10101000.00000001.01100101 converts to 192.168.1.101.
Outlines
📊 Understanding Decimal Place Values
This paragraph introduces the concept of positional notation in the decimal (base-10) number system using the example of the number 2168. It breaks down the place values as powers of ten, such as the ones, tens, hundreds, and thousands place, showing how each contributes to the overall value of the number. The author explains how each digit represents a multiplication of the digit with the corresponding power of ten. The discussion includes an example of how numbers are added together in their expanded form (e.g., 2000 + 100 + 60 + 8). This provides a foundation for understanding decimal notation as we use it in everyday counting.
💡 Introduction to Binary Place Values
This section contrasts the decimal system with the binary (base-2) system. In binary, only two digits (0 and 1) are used. It explains how binary place values correspond to powers of two, starting from 2^0 (1) up to higher powers like 2^7 (128). The paragraph includes a detailed example of converting the decimal number 168 into binary by examining which powers of two fit into the number and assigning 1s or 0s to the corresponding place values. This results in the binary representation 10101000 for the decimal number 168. The idea of 8 bits forming a byte in computer processing is also introduced.
Mindmap
Keywords
💡Positional Notation
💡Base-10 (Decimal System)
💡Base-2 (Binary System)
💡Powers of Ten
💡Powers of Two
💡Bit
💡Byte
💡Binary to Decimal Conversion
💡Decimal to Binary Conversion
💡IP Address
Highlights
Introduction to binary to decimal conversion and overview of positional notation in base 10.
Explanation of place values in the decimal system: ones, tens, hundreds, thousands, etc.
Demonstration of breaking down the number 2168 by place values, showing how it's composed of 2000, 100, 60, and 8.
Clarification that the decimal system is a base 10 system using powers of 10, with digits from 0 to 9.
Comparison between decimal (base 10) and binary (base 2) number systems.
Binary system explained: only two possible values (0 and 1) and place values as powers of 2 (1, 2, 4, 8, 16, 32, etc.).
Illustration of converting the decimal number 168 into binary by assigning 1 or 0 to binary place values.
Step-by-step process of converting 168 to binary: placing 1s and 0s in the appropriate positions (128, 32, and 8).
Explanation of how 168 in decimal equals 10101000 in binary.
Introduction to converting binary numbers back to decimal using place values.
Demonstration of converting the binary number 01101101 to decimal by adding up place values (64, 32, 8, 4, 1).
Conversion result: the binary number 01101101 equals 109 in decimal.
Introduction to IP addresses in binary and how to convert them to decimal.
Breakdown of a 32-bit IP address into four octets for conversion.
Example conversion of binary IP address 11000000.10101000.00000001.01100101 to decimal 192.168.1.101.
Transcripts
this video i'm going to discuss binary
to decimal conversion but before i do
this i want to take a look at positional
notation or place values i have the
number
2168 here
if we look at the place values of the
number 2168
we can see that the place values have
the ones place
the tens place the hundreds place the
thousands place ten thousand hundred
thousand and million these are the place
values of the base 10 decimal number
system
you can see that we have the number two
in the one thousands place so we have
two one thousands we have a one in the
hundreds place for one hundred we have
six in the tens place for sixty and we
have eight in the ones place for eight
so effectively we have two one thousands
one one hundred
six tens for sixty
and eight ones for eight
now when we're talking about the place
values in the decimal number system
we're talking about the powers of ten
you can see that the ones place is the
ten to the zero
the tens place ten to the one the
hundreds place ten to the two or ten
times ten which is a hundred the
thousands place is the ten to the three
or ten times ten times ten
and so on and so forth so you can see
that the place values
are based on powers of ten if we look at
the number 2106
then in long form we can see that
effectively we have two one thousands
one one hundred
six tens
and eight ones and two thousand plus one
hundred plus sixty plus eight
totals two thousand one hundred and
sixty eight
this is the type of counting and
addition that we learn as children
the decimal system
is base ten
it's based on the fact that you have one
powers of ten
but more importantly you have ten
characters or ten numerals in this
counting system from zero all the way up
to nine so that means that in each place
value you can have anywhere from the
number zero up to the number nine in
other words if i had the number
9168 i'd simply replace the two here
with a nine and now i have
nine
one thousands totaling nine thousand
in the one thousands place
so in any one of these place values you
can have the number zero all the way up
to 9. this is the base 10 decimal number
system
if we consider binary and look at it in
the same light as decimal
binary is a base 2 number system there's
only two characters or two numbers zero
and one
so under the place values
we can only have zeros or ones
the place values go from one which is
two to the zero
to two two to the one four two to the
two eight two to the three or two times
two times two is eight
two times two times two times two is
sixteen that's two to the fourth power
place value of sixteen
the thirty-two's place the sixty-fours
place and the one twenty eighths place
notice that i extended the table to
eight place values that's because eight
bits is an important grouping of numbers
eight bits makes a byte in computer
processing so now i have the place
values
for essentially 8 bits
if i want to write the number
168 in binary i just have to find the
corresponding place values and plug in
either a one or a zero
so i'll go to the hundred and twenty
eighths place and ask myself do i need
128 to reach 168 yes i do so i'll put a
one there
now do i need a 64. i already have a 128
if i add 64
i would get 192 because 128 plus 64 is
192. so the answer is no so i put a zero
i still have 128 now now do i need a 32
128 plus 32 is 160 so yes
i could use a 1 here
now i have 160
do i need a 16 no that would make 176
which would go over my target number of
168.
i'll put a zero here
what about an eight if i add an eight
i'll hit the number perfectly 128 plus
32 plus eight is 168. i'll follow this
up with zeros in the fourth place
the two's place
and the ones place
and 168 in binary equals one zero one
zero one zero zero zero
i now have
one one hundred and twenty eight
i have one thirty two
and i have one eight and a hundred and
twenty eight plus thirty two plus eight
equals a hundred 168.
if we go to the next slide
you can see now that i'm now charged
with converting the number 0 1 1 0
1 1 0 1
to decimal
if i want to go the opposite way and
convert this binary number to decimal
all i need to do is plug it into the
place values
i'll put it in here 0
1
1
0.
1 1
0
1
and then add it up
i have a 64
and i have a 32
64 plus 32 is
96. i have an eight that makes a hundred
and four
plus four makes a hundred and eight
plus one makes a hundred and nine
this number converted to decimal is the
number one hundred and nine
now let's look at a full ip address in
binary
i'll go to my next slide
and you can see in this next slide i now
have
a 32-bit ip address
4 octets
or 32 bits total
if i want to convert this binary ip
address to decimal all i need to do is
count up each individual octet
let's start with the first one
right here
we can see that one
one
zero
zero zero zero zero 0
128 plus 64 is
192.
now the next octet has 1 0 1 0 1 let's
do that one
zero
one
zero one and then all zeros
if we count up the numbers
128
plus 32 is 160 plus eight is one sixty
eight
the next octet is all zeros
with a one in the last place in the ones
place
this is easy this is the number
one
all zeros and a one in the ones place
makes the number one
and then finally we have a number here
i'll plug it in here into my table
[Music]
and i have the number zero one one zero
zero
one zero one
we can see that 64 plus 32 we've already
said
is 96
plus four
is a hundred plus one
is one hundred and one
so the conversion of this binary ip
address to decimal is 192.168.1.101
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