binary logic lets think about the binary!. what is binary? computers use binary as it’s a lot...

Binary Logic

Lets think about the Binary!

What is Binary?

Computers use binary as it’s a lot simpler!

Each CPU is made up of millions of transistors which can only have TWO states (ON/OFF).We will be thinking of it as either 1 or 0.

Anything can be converted into a binary number so a computer can understand, process and store it.

How binary is calculated?

1 2

4 8

We have FOUR shapes worth a different amount

but ONLY ONE of each.

How do we get 1?

1

All we need is ONE GREEN TRIANGLE!


1 2

4 8



How do we get 2?

All we need is ONE BLUE CIRCLE!

2


1 2

4 8



How do we get 3?

All we need is ONE GREEN TRIANGLE and ONE BLUE CIRCLE!

21


1 2

4 8



How do we get 5?

All we need is ONE GREEN TRIANGLE and ONE ORANGE SQUARE!

1 4


1 2

4 8



How do we get 7?

All we need is ONE GREEN TRIANGLE and ONE ORANGE SQUARE!

1 2 4


1 2

4 8



What’s the highest number we can make?

1 + 2 + 4 + 8 = 15

1 2 4 8

Binary Numbers

0 0 0 10 0 1 00 0 1 10 1 0 0 0 1 0 10 1 1 0

If we use a shape we mark it as ‘1’ otherwise it’s a ‘0’

1248 TOTAL

123456

How many 8’s can fit into 5?The answer can be 1 or 0.

Click to continue…

8 fits into 5 zero times…So we put a 0 in the 8 column.


8 4 2 1

Let’s take the number 5 and work out the binary representation…

5 0

Does 4 fit into 5?1 or 0 times?


4 fits into 5! So we put a 1 in the 4 column.


1

We then have to take the 4 we have noted away from the original number…


1This leaves 1 left over – we will nowtest our numbers against 1 instead.


How many 2’s fit into 1?


2 is larger than 1, so we put a zero in the 2 column.


0

Does 1 fit into 1?The answer can be 1 or 0.


1

1 fits into 1 exactly So, one last time, a 1 goes in the final column.


So 5 = 0101 in 4-bit binary.We can check we have the answer right by adding

the columns that hold a 1.4 + 1 = 5, so 0101 is correct.

Practice!

Complete Binary Worksheet 1

What are binary numbers used for?

Anything the computer needs!We have been calculating Nibbles (4 bits) but

computers usually work in Bytes (8 bits).

8 4 2 1

We know what the FIRST FOUR bits stand for, what do you think the NEXT FOUR stand for?

163264128

8 4 2 1

What is the binary number for 129?

163264128

124864 32 16128

OR1 0 0 0 0 0 0 1

8 4 2 1

What is the binary number for 71?

163264128

124864 32 16128

0 1 0 0 0 0 1 1

Practice!

Complete Binary Worksheet 2

Gates

We know that BITS are either 1 or 0 but there are “gates” which can change the value.

Do you like to play football?1 = Yes0 = No

NOT

5 say “Yes” &3 say “No”

Do you not like to play football?

1 = Yes0 = No

5 say “No” &3 say “Yes”

1 becomes 0 &0 becomes 1

GatesDo you like to play

playstation?1 = Yes0 = No

AND5 say “Yes” &

3 say “No”

Do you like to play playstation AND

sing?1 = Yes0 = No

1 says “Yes” &7 say “No”

Both questions must be ‘1’ to

output ‘1’

Do you like to sing?

1 = Yes0 = No


GatesDo you like to play

playstation?1 = Yes0 = No

OR5 say “Yes” &

3 say “No”

Do you like to play playstation OR sing?

1 = Yes0 = No

1 says “Yes” &7 say “No”One or more

questions must be ‘1’ to output

‘1’

Do you like to sing?

1 = Yes0 = No


Truth Tables

We sometimes represent these gates on a Truth Table, e.g.:

Copy the truth table into your notes and also create the truth tables for the NOT and OR gates

Practice!

Go onto http://logic.ly/demo and complete the following tasks on one sheet:a) Create an A OR B circuitb) Create (A OR B) and Cc) Create (Not A) AND Bd) Create (Not (A AND B)) OR CPrint out this one page by taking a screen shot and create the truth tables for these tasks

A, B & C are light switches

http://logic.ly/demo

binary logic lets think about the binary!. what is binary? computers use binary as it’s a lot...

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