TOPICS:  Introduction  Place Value  Binary  Decimal conversion  Decimal  Binary conversion  Related terms  Quiz

Computers are used daily by nearly everyone at home, school and work, for business, education and entertainment.

How do computers work? Are they really smart?

Computers don’t really think. They are electronic equipment made up of electrical circuits that are either “ON” or “OFF”

How do computers store information? Computers store information as strings of electrical impulses. They are either “ON” (there is electricity) or they are “OFF” (there isn’t electricity). The number “1” is “ON” and the number “0” is “OFF”.

0 and 1 All data and programming is changed to zeros and ones. Each of these digits, either 0 or 1 is a BIT… That is short for Binary digit

Bits & Bytes While each piece A string of of data, 0 or 1, data that is a is a BIT, specific number of bits is a BYTE BYTES are strings of 8 BITS. That is, a string of eight 0s and 1s together. Example: or

BYTES!

LET’S REVIEW What is a BINARY DIGIT? BYTEBIT

OOPS!!! Try again!

YES!

LET’S REVIEW What is a string of BINARY DIGITS? BYTE BIT

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YES!

Because computers use only these two numbers, we say they operate on a BINARY number System.

BINARY is a number system based on TWO numbers, 0 and 1, instead of the base 10 number system we use every day.

The base number system determines what digits are used. The base 10 system we commonly use includes the digits and 0

Computers use 0 and 1 exclusively, so they use base 2, or a BINARY system.

Every number base uses digits 0 to one number less than the number base. So… Base 4 uses 0, 1, 2 and 3 Every number base uses digits 0 to one number less than the number base. So… Base 4 uses 0, 1, 2 and 3 Base 8 uses 0, 1, 2, 3, 4, 5, 6, and 7

What digits are in a binary number system? CHECK UP  0 - 1

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YES!

How do you change a number to binary? First you have to understand how we determine the value of numbers. How do you change a number to binary? First you have to understand how we determine the value of numbers.

In whatever number system you are using, the VALUE of the number depends on the PLACE it is in. You learned this as PLACE VALUE. hundred’s place ten’s place one’s place In whatever number system you are using, the VALUE of the number depends on the PLACE it is in. You learned this as PLACE VALUE. hundred’s place ten’s place one’s place

That is, 2 is different than 20 or 200, because the 2 is in different places, which changes the VALUE. The zeroes just fill in empty columns. But place value is actually the POWER of the base… the one’s place is 10 0 the ten’s place is 10 1 the hundred’s place is 10 2.

When you learned numbers you read the VALUE of numbers by adding the place values…. 1,234 = 1 x 1000 = 1000 (or 1 x10 3 ) + 2 x 100 = 200 (or 2 x 10 2 ) + 3 x 10 = 30 (or 3 x 10 1 ) + 4 x 1 = 4 (or 4 x 10 0 ) = 1,234 When you learned numbers you read the VALUE of numbers by adding the place values…. 1,234 = 1 x 1000 = 1000 (or 1 x10 3 ) + 2 x 100 = 200 (or 2 x 10 2 ) + 3 x 10 = 30 (or 3 x 10 1 ) + 4 x 1 = 4 (or 4 x 10 0 ) = 1,234

You may remember this was called EXPANDED NOTATION

In BINARY, it works the same way, but the place values are in powers of 2 instead of Powers of

Place value is in powers of

To find the value of a binary number, just add up the place values. It is helpful to write the place values, and then add the number. Try this example: Adding the values = = 21 To find the value of a binary number, just add up the place values. It is helpful to write the place values, and then add the number. Try this example: Adding the values = = 21

When you add up the place values, you get the number in base 10 (conventional numbers). Example: = = 9

Try this again with the number 1110 Example: = = 14

Try this again with another number and greater powers of = 77 Try this again with another number and greater powers of = 77

Now try it on your own: Here are the place values: What is the number? Now try it on your own: Here are the place values: What is the number? Check answer here 49

Now try it on another one! Here are the place values: Now try it on another one! Here are the place values: Check answer here 37

You need to compare the PLACE VALUES of BINARY NUMBERS to the decimal number you are wanting to convert. What is the biggest binary number that is in it?

Try again with a bigger number: > 32 but < – 32 = = = – 2 = Check  Is = 47? YES!!! Try again with a bigger number: > 32 but < – 32 = = = – 2 = Check  Is = 47? YES!!!

Try again with a different number: > 16 but < – 16 = = Check  Is = 18 YES!!! Try again with a different number: > 16 but < – 16 = = Check  Is = 18 YES!!!

Now you try binary  decimal Change 1010 to base 10 (use the place values) Now you try binary  decimal Change 1010 to base 10 (use the place values) Check answer here 10

Try binary  decimal again Change to base 10 (use the place values) Try binary  decimal again Change to base 10 (use the place values) Check answer here 19

Now decimal  binary Change 35 to binary (subtract the place values from the number) Now decimal  binary Change 35 to binary (subtract the place values from the number) Check answer here

Now decimal  binary Change 39 to binary (subtract the place values from the number) Now decimal  binary Change 39 to binary (subtract the place values from the number) Check answer here

You can see that if 35 is a SIX DIGIT number in binary, then binary numbers get really BIG really FAST! That is why they have prefixes like…

KILO as in kilobyes which is 2 10 bytes MEGA as in megabytes which is 2 20 bytes And GIGA as in gigabytes which is 2 30 bytes This is to show how many binary digits are used. These are commonly used for file sizes and storage. KILO as in kilobyes which is 2 10 bytes MEGA as in megabytes which is 2 20 bytes And GIGA as in gigabytes which is 2 30 bytes This is to show how many binary digits are used. These are commonly used for file sizes and storage.

Then there are even BIGGER prefixes  TERA = 2 40 PETA = 2 50 EXA = 2 60 ZETTA = 2 70 And YOTTA = 2 80 Then there are even BIGGER prefixes  TERA = 2 40 PETA = 2 50 EXA = 2 60 ZETTA = 2 70 And YOTTA = 2 80

And then there is GOOGOL 1 with 100 zeros!! And then there is GOOGOL 1 with 100 zeros!!

CHECK UP! Match the answers. What is a binary digit? What is a string of binary digits? CHECK UP! Match the answers. What is a binary digit? What is a string of binary digits? byte bit Float your mouse here to find the pen you can use to draw a line to the correct answer.* * You will need to “unclick” the pen tool and click the “arrow” tool to go on to the next slide. Be sure to “discard” annotations when asked.

CHECK YOUR ANSWER! Match the answers. What is a binary digit? What is a string of binary digits? CHECK YOUR ANSWER! Match the answers. What is a binary digit? What is a string of binary digits? byte bit

What number system uses only digits 0 and 1? binary decimal

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YES!

Convert the following binary numbers to decimal Convert the following binary numbers to decimal Check answer here Check answer here

Convert the following decimal numbers to binary Convert the following decimal numbers to binary Check answer here Check answer here

Now, answer this…. There are only 10 kinds of people, those who understand binary, and those who don’t. Which are you? Now, answer this…. There are only 10 kinds of people, those who understand binary, and those who don’t. Which are you?

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