Chapter 5 Flashcards
2 types of Logic Systems
- Combinational Circuit
- Sequential Circuit
- Consists of Logic gates only
- The output is dependent only on the input of the logic levels.
Combinational Circuit
- Consists of logic gates and Memory elements.
- The output of the system is not only dependent on its inputs but also dependent on the present state of the output which is stored in its memory.
Sequential Circuit
The characteristic of a logic circuit allows us to use Boolean Algebra as a tool for analyzing and designing a digital circuit or a digital system.
Readings
________________ is a simple mathematical tool that allows us to describe the relationship between a logic circuits output to its input. It is represented by algebraic equation also called the _______________
Boolean algebra, Boolean expression.
A Boolean variable is a quantity that may be equal to either ________
0 or 1.
A _______________ are often used to represent the voltage level present on a wire or the input and output terminals of a given logic circuit.
Boolean variable
In boolean algebra, ___________ is a symbol used to represent an action, a condition, or data. A single variable can only have a value of 1 or 0.
Variable
represents the inverse of a variable and is indicated with an overbar or a prime (‘). So the complement of A is A’.
Complement
A __________ is a variable or its complement.
Literal
In Boolean algebra, ______________ is equivalent to the ______ operation. The product of literals forms a product term. The product term will be 1 only if all of the literals are 1.
multiplication, AND
The Theorems in Boolean algebra are very useful especially when we need to simplify a ____________________. Using this technique we can transform the given into a meaningful equivalent expression.
complex Boolean Expression
are applied to addition and multiplication.
Commutative Laws
These law indicates that the order in which we ORed or ANDed the two variables is not important; the result is the same.
Commutative Laws
are also applied to addition and multiplication.
Associative Laws
This theorem states that we can group the variable in an AND expression or OR expression in any way we want.
Associative Laws
is the factoring law.
Distributive Law
These law states that an expression can be expanded by multiplying term by term just like in ordinary algebra. And also a common variable can be factored from an expression.
Distributive Law
Two of the most important theorems of Boolean algebra were contributed by a great mathematician named De Morgan.
DeMorgan’s 1st Theorem, DeMorgan’s 2nd Theorem
“The complement of a product of variables is equal to the sum of the complemented variables.”
DeMorgan’s 1st Theorem
“The complement of a sum of variables is equal to the product of the complemented variables.”
DeMorgan’s 2nd Theorem
Any expression can be implemented by the basic logic gates; AND, OR and Inverter gate. But it is also possible that these three basic logic gates are implemented using NAND gate and NOR gate. That is why it is called the _______________
Universal gates.
