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1,2,3,4,5,6,7,8,9,10,11
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Слайды и текст к этой презентации:
№1 слайд
Содержание слайда: Logical expressions
simplify a logic circuit/expression using Boolean algebra
№2 слайд
Содержание слайда: Review
Last lesson we learned logical operators. Name which of them do you remember?
What is ALU?
Why do we need to know logical expressions?
№3 слайд
Содержание слайда: Main logical operators and their truth tables
And Or Nand Xor Nor
№4 слайд
Содержание слайда: Notice!!
When we write equations
+ is And
* is Or
is Not
___
A+B is Nand
___
A*B is Nor
№5 слайд
Содержание слайда: Simplifying boolean equations with Truth Tables
A common question is to give you a complex boolean equation, which you will then have to work out a simpler exact equivalent. This is useful when you are designing circuits and want to minimise the number of gates you are using or make circuits that only use particular types of gates. To simplify boolean equations you must be familiar with two methods. You can normally use either, but try to master both:
Truth tables
Boolean algebra - identities and De Morgan’s Law
№6 слайд
Содержание слайда: Simplifying boolean equations with Truth Tables
_______
A + notB
First of all we need to draw a truth table for A and B
Then we need to add there notB
After that we calculate A + notB
And finally we apply NOT for our equation A + notB
№7 слайд
Содержание слайда: And we get this
№8 слайд
Содержание слайда: Exercise 1
Simplify the following equation yourself using Truth table:
_______
A * notB
№9 слайд
Содержание слайда: Answer 1
№10 слайд
Содержание слайда: De Morgan’s law
Not (A and B) is the same as Not A or Not B.
____ _ _
A + B = A * B
Not (A or B) is the same as Not A and Not B.
____ _ _
A * B = A + B
№11 слайд
Содержание слайда: Prove
Let's prove that I'm not lying to you by creating a truth table to prove that ____ _ _
A * B = A + B
№12 слайд
Содержание слайда: Exercise 2
Prove the second De Morgan’s Law with Truth table
____ _ _
A + B = A * B
№13 слайд
Содержание слайда: Answer 2
№14 слайд
Содержание слайда: Now do some exercises on the paper sheets
№15 слайд
Содержание слайда: Reflection
Why do we need simplification?
How can it help circuits?
What way of simplification you like better Truth tables or De Morgan’s rule?