Digital Logic Design 2 Flashcards
Define Duality Principle
A valid algebraic expression can be derived from another by interchanging the operators and identity elements
How do you find the dual?
Interchange · and + operators
Replace 1’s with 0’s and vice versa
What are the 6 basic theorems?
Theorem 1
x + x = x
x · x = x
Theorem 2
x + 1 = 1
x · 0 = 0
Theorem 3, involution
(x’)’ = x
Theorem 4, associative law
x + (y + z) = (x + y) + z
x(yz) = (xy)z
Theorem 5, DeMorgan’s theorem
(x + y)’ = x’ · y’
(x · y)’ = x’ + y’
Theorem 6, absorption
x + xy = x
Using the numbers 1-4 (1 is highest) what is the precedence for boolean operators?
- ()
- NOT ‘
- AND ·
- OR +
What is a boolean function?
Are algebraic expressions formed with: Binary variables Binary operators OR (+) and AND (·) Unary operator NOT ( ’) parentheses equal sign
How can boolean functions be represented?
As a truth table
Boolean functions can be represented with a logic diagram composed of AND, OR, and NOT gates
What is algebraic minimization?
attempt to use postulates and theorems to reduce a boolean function down to its simplest representation (minimize literals and terms)
Define literal
A primed or unprimed variable
Each literal in a function corresponds to an input to a gate
Define term
A term consists of one or more literals grouped together with an AND or OR operator
Each term is implemented with a gate
Why is minimization important?
In designing logic, we often begin with a truth table
From this a boolean function is obtained
From this a hardware design is made
Thus when we minimize the function we minimize the hardware design, this in turn
Reduces cost Reduces power consumption Reduces package count Increases speed Simplifies testing and debugging
What is the complement of a function?
The complement of a function f is f’ (primed)
How can you find a complement of a function
for a truth table invert 0’s and 1
algebraically use DeMorgan’s Theorem
How do you find the complement of a function involving deMorgan’s Theorem?
Complement the entire expression
Apply DeMorgan’s theorem repeatedly
What is the short cut method of DeMorgan’s Theorem?
Form the dual of the function
Complement each literal
