Circuit simplification student version

Circuit simplification student version - EC262 Topic 3:...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
1 EC262 Topic 3: Circuit Simplification Logical Equivalence Two Boolean expressions are logically equivalent iff they have identical output values for all possible combinations of values for the inputs. So, to test if two Boolean expressions A and B are logically equivalent, we construct truth tables for A and B . If the truth values of A and B match for all rows in the truth table, then A and B and logically equivalent. Example: Are p and ( ) '' p logically equivalent? What implication does this have for logic circuits? What can we say about these two logic circuits? p q p q Circuit 1 Circuit 2 Example. Show that a + a b is logically equivalent to a + b . What’s the point? Well, draw the circuit for a + a b and draw the circuit for a + b . The two circuits above do the same thing. Which is better and why?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Example. Show that a + bc is logically equivalent to ( a + b )( a + c ). What’s the point? Well, draw the circuit for a + bc and draw the circuit for ( a + b )( a + c ). The two circuits above do the same thing. Which is better and why? Example. Your friend says that a ( a + b ) = ab . Is he correct?
Background image of page 2
3 Properties of Switching Algebra A number of logical equivalences are well known—so well known that they are plastered on the inside cover of your textbook—and are reprinted below. From Alan Marcovitz, Introduction to Logic Design , 3 rd ed, McGraw Hill, 2010 So, each of these properties can be proven by showing the logical equivalence of the Boolean expressions on each side of the equals sign, using the approach from the previous page. In fact, the example on the bottom of page 1 proved Property P10a from the table above and the example on the top of page 2 proved Property P8b. Again, the point: If we have a Boolean expression a + a b , we can use Property 10a to immediately replace this with the expression a + b . Ditto with the properties in the rest of the table.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Note also that the properties are general in that each of the terms can be replaced by more complex expressions. For example, Property 1a, says that a + b = b + a . If we substitute xy for a and w z for b , Property 1a becomes xy + w z = w z + xy . Now we are at last ready to address Task 5 from last lecture. ( Task 5 ) Given a digital logic circuit, design a simpler digital logic circuit that performs the equivalent function. To accomplish this: Find the Boolean expression that corresponds to this logic circuit (TASK 1 from last lecture).
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/27/2012 for the course ECE 200 taught by Professor Nasis during the Spring '08 term at Drexel.

Page1 / 12

Circuit simplification student version - EC262 Topic 3:...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online