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Maurice Karnaugh, a telecommunications engineer, developed the Karnaugh map at Bell Labs in 1953 while designing digital logic based telephone switching circuits. Now that we have developed the Karnaugh map with the aid of Venn diagrams, let's put it to use. Karnaugh maps reduce logic functions more quickly and
Karnaugh Maps. • Applications of Boolean logic to circuit design. – The basic Boolean operations are AND, OR and NOT. – These operations can be combined to form complex expressions, which can also be directly translated into a hardware circuit. – Boolean algebra helps us simplify expressions and circuits. • Karnaugh
Karnaugh Maps (K-map). • Alternate representation of a truth table. ?Red decimal = minterm value. • Note that A is the MSB for this minterm numbering. ?Adjacent squares have distance = 1. • Valuable tool for logic minimization. ?Applies most Boolean theorems & postulates automatically (when procedure is followed). B. A.
Introduction to Karnaugh Maps. Review. So far, you (the students) have been introduced to truth tables, and how to derive a Boolean circuit from them. We will do an example. Consider the truth table for a basic 2-input multiplexer. We can view the truth table as a sort of specification which says what a circuit should do.
E1.2 Digital Electronics I. 5.1. Lecture 5: Logic Simplication &. Karnaugh Map. Professor Peter Cheung. Department of EEE, Imperial College London. (Floyd 4.5-4.11). (Tocci 4.1-4.5). Cot 2007. E1.2 Digital Electronics I. Points Addressed in this Lecture. • Standard form of Boolean Expressions. – Sum-of-Products (SOP),
Can you make a counter which count from 3 to 8 ? • Repeat the 7 segment BCD display example if we don't care about the output values for illegal input from 10 to 15. (Note that in that example we took X="0" for illegal input. • How does MUX work ? Can you make it with using some simple logic ? • Can you make 1 bit
Karnaugh Maps (K-maps). • Karnaugh maps -- A tool for representing Boolean functions of up to six variables. • K-maps are tables of rows and columns with entries represent. 1`s or 0`s of SOP and POS representations.
Karnaugh Maps. ?Objectives. This section presents a technique for simplifying logical expressions. It will: ? Define Karnaugh and establish the correspondence between. Karnaugh maps and truth tables and logical expressions. ? Show how to use Karnaugh maps to derive minimal sum- of-products and product-of-sums
Step 1: Draw the Karnaugh map that represents the expression by placing a mark in each appropriate square. Step 2: “Cover" the marked boxes as best you can with ovals. Allowed coverings for this setup are limited to 2x1 rectangles. This example is covered by one 2x1 rectangle. Step 3: Expressions/rectangles that are
Department of Communication Engineering, NCTU. 3. Logic Design. Unit 5 Karnaugh Map. Sau-Hsuan Wu. ? Switching functions can generally be simplified by using. Boolean algebraic techniques. ? Two problems arise when algebraic procedures are used. ? The procedures are difficult to apply in a systematic way.
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