Understanding Karnaugh Maps Part 1 - Introducing Literals, Min-terms, Max-terms, Canonical Expressions, Sum-Of-Product (SOP) and Product-Of-Sum(POS) Forms and Expansions



Number System



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  Digital Electronics : Karnaugh Maps Part 1

 

 
K Maps Tutorial, Digital Electronics

Here's a quick walk through of the ideas which will be introduced in this tutorial






• Literals :

A literal is a single logic variable or its complement. For example— X, Y, A’, Z, X’, etc.

• Minterms: 

A minterm is the product of all the literals with or without complement involved in a logic system.




If X=0, Y=0 minterm would be X’Y’



• Maxterm: 

A maxterm is the sum of all the literals with or without complement involved in a logic system.








• Canonical expressions

A Boolean expression containing entirely of minterms or maxterms is known as canonical expression. These are of two types—

 • Sum Of Product(SOP form)

It is the sum of all the minterms that result in a true value of the output variable. For example—




• Product Of Sums(POS form)

It is the product of all the maxterms that result in a false value of the output variable. For example—






• Shorthand notation




• For minterm representation







6

•  For maxterm representation

T



M2











Here's a list of all the tutorials we currently have in this area - Introductory Digital Electronic Circuits and Boolean logic

 Introduction to the Number System : Part 1
Introducing number systems. Representation of numbers in Decimal, Binary,Octal and Hexadecimal forms. Conversion from one form to the other.
 Number System : Part 2
Binary addition, subtraction and multiplication. Booth's multiplication algorithm. Unsigned and signed numbers. 
Introduction to Boolean Algebra : Part 1
 Binary logic: True and false. Logical operators like OR, NOT, AND. Constructing truth tables. Basic postulates of Boolean Algebra. Logical addition, multiplication and complement rules. Principles of duality.  Basic theorems of boolean algebra: idempotence, involution, complementary, commutative, associative, distributive and absorption laws. 
Boolean Algebra : Part 2
De-morgan's laws. Logic gates. 2 input and 3 input gates. XOR, XNOR gates. Universality of NAND and NOR gates. Realization of Boolean expressions using NAND and NOR. Replacing gates in a boolean circuit with NAND and NOR.
  Understanding Karnaugh Maps : Part 1Introducing Karnaugh Maps. Min-terms and Max-terms. Canonical expressions. Sum of products and product of sums forms. Shorthand notations. Expanding expressions in SOP and POS Forms ( Sum of products and Product of sums ). Minimizing boolean expressions via Algebraic methods or map based reduction techniques. Pair, quad and octet in the context of Karnaugh Maps.

Karnaugh Maps : Part 2
Map rolling. Overlapping and redundant groups. Examples of reducing expressions via K-Map techniques.
 Introduction to Combinational Circuits : Part 1
Combinational circuits: for which logic is entirely dependent of inputs and nothing else. Introduction to Multiplexers, De-multiplexers, encoders and decoders.Memories: RAM and ROM.  Different kinds of ROM - Masked ROM, programmable ROM. 
 Combinational Circuits : Part 2
 Static and Dynamic RAM, Memory organization.
Introduction to Sequential Circuits : Part 1
Introduction to Sequential circuits. Different kinds of Flip Flops. RS, D, T, JK. Structure of flip flops. Switching example. Counters and Timers. Ripple and Synchronous Counters. 
Sequential Circuits : Part 2
ADC or DAC Converters and conversion processes. Flash Converters, ramp generators. Successive approximation and quantization errors. 
 


 



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