Topic 2 Boolean Algebra - Outline Fundamental Boolean...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Topic 2 Boolean Algebra Akash Kumar Outline Fundamental Boolean operations Deriving logic expressions from truth tables SOP and POS expressions Rules for deriving SOP and POS expressions Boolean Identities Simplifying logic expressions using Boolean identities Karnaugh maps Obtaining MSOP’s and MPOS’s from K-maps Don’t care conditions 2 Boolean Algebra Boolean algebra is the basic math used in digital circuits and computers. A Boolean variable takes on only 2 values: {0,1} , {T,F}, {Yes, No}, etc. There are 3 fundamental Boolean operations: AND, OR, NOT 3 Fundamental Boolean Operations AND OR NOT Z=A*B (AB) Z=A+B Z= Ā Truth Table Truth Table Truth Table A B Z B Z Z ABZ 000 010 100 111 011 101 AZ 01 10 5
Background image of page 1

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

View Full DocumentRight Arrow Icon
Boolean Algebra A truth table specifies output signal logic values for every possible combination of input signal logic values In evaluating Boolean expressions, the Operation Hierarchy is: 1) NOT 2) AND 3) OR . Order can be superseded using ( … ) Example: What is the value of ? ) ( ) ( D B C B A Z F D B C F D B C F F D B C F T Z ) ( ) ( ) ( ) ( ) ( T D T C F B T A , , , 6 Deriving Logic Expressions From Truth Tables What is the Boolean expression for Z? 7 Light must be ON when both switches A and B are OFF, or when both of them are ON. Logic Function SW.A SW.B Z (light) Truth Table: ABZ 001 010 100 111 Min-terms and MAX-terms Min-terms AND term of all input variables. For variables with value 0, apply complements MAX-terms OR factor with all input variables For variables with value 1, apply complements 8 A B Z Min-terms MAX-terms ܣ.ܤ ܣ൅ܤ ܣ. ܤ ܣܤ Min-terms and MAX-terms A function with n variables has 2 n min-terms (and MAX-terms) – exactly equal to the number of rows in truth table Each min-term is true for exactly one combination of inputs Each MAX-term is false for exactly one combination of inputs 9 A B Z Min-terms MAX-terms ܣ. ܤ ܣܤ
Background image of page 2
Deriving Logic Expressions From Truth Tables Two equivalent logic expressions can be derived from Truth Tables: 1. Sum-of-Products (SOP) expressions: Several AND terms OR’d together, e.g. 2. Product-of-Sum (POS) expressions: Several OR terms AND’d together, e.g. ABC C B A C B A ) )( ( C B A C B A 10 Rules for Deriving SOP Expressions 1. Find each row in TT for which output is 1 (rows 1 & 4) 2. For those rows write a min-term of all input variables. 3. OR together all min-terms found in (2): Such an expression is called a Canonical SOP AB B A Z 11 A B Z Min-terms MAX-terms 001 ܣ.ܤ ܣ൅ܤ 010 100 ܣ. ܤ 111 ܣܤ Rules for Deriving POS Expressions 1.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 14

Topic 2 Boolean Algebra - Outline Fundamental Boolean...

This preview shows document pages 1 - 4. Sign up to view the full document.

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